Series in Banach Spaces: Conditional and Unconditional Convergence
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1997
|
| Schriftenreihe: | Operator Theory Advances and Applications
94 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problems studied. The phenomenon that a numerical series can change its sum when the order of its terms is changed is one of the most impressive facts encountered in a university analysis course. The present book is devoted precisely to this aspect of the theory of series whose terms are elements of Banach (as well as other topological linear) spaces. The exposition focuses on two complementary problems. The first is to char acterize those series in a given space that remain convergent (and have the same sum) for any rearrangement of their terms; such series are usually called uncon ditionally convergent. The second problem is, when a series converges only for certain rearrangements of its terms (in other words, converges conditionally), to describe its sum range, i.e., the set of sums of all its convergent rearrangements |
| Beschreibung: | 1 Online-Ressource (VIII, 159 p) |
| ISBN: | 9783034891967 9783034899420 |
| DOI: | 10.1007/978-3-0348-9196-7 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042422323 | ||
| 003 | DE-604 | ||
| 005 | 20160616 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1997 |||| o||u| ||||||eng d | ||
| 020 | |a 9783034891967 |c Online |9 978-3-0348-9196-7 | ||
| 020 | |a 9783034899420 |c Print |9 978-3-0348-9942-0 | ||
| 024 | 7 | |a 10.1007/978-3-0348-9196-7 |2 doi | |
| 035 | |a (OCoLC)879623219 | ||
| 035 | |a (DE-599)BVBBV042422323 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 510 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Kadec, Michail I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Series in Banach Spaces |b Conditional and Unconditional Convergence |c by Mikhail I. Kadets, Vladimir M. Kadets |
| 264 | 1 | |a Basel |b Birkhäuser Basel |c 1997 | |
| 300 | |a 1 Online-Ressource (VIII, 159 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Operator Theory Advances and Applications |v 94 | |
| 500 | |a Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problems studied. The phenomenon that a numerical series can change its sum when the order of its terms is changed is one of the most impressive facts encountered in a university analysis course. The present book is devoted precisely to this aspect of the theory of series whose terms are elements of Banach (as well as other topological linear) spaces. The exposition focuses on two complementary problems. The first is to char acterize those series in a given space that remain convergent (and have the same sum) for any rearrangement of their terms; such series are usually called uncon ditionally convergent. The second problem is, when a series converges only for certain rearrangements of its terms (in other words, converges conditionally), to describe its sum range, i.e., the set of sums of all its convergent rearrangements | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Konvergente Reihe |0 (DE-588)4304017-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Banach-Raum |0 (DE-588)4004402-6 |D s |
| 689 | 0 | 1 | |a Konvergente Reihe |0 (DE-588)4304017-2 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Kadec, Vladimir M. |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-0348-9196-7 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027857740 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153096616542208 |
|---|---|
| any_adam_object | |
| author | Kadec, Michail I. |
| author_facet | Kadec, Michail I. |
| author_role | aut |
| author_sort | Kadec, Michail I. |
| author_variant | m i k mi mik |
| building | Verbundindex |
| bvnumber | BV042422323 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879623219 (DE-599)BVBBV042422323 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-9196-7 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03085nmm a2200481zcb4500</leader><controlfield tag="001">BV042422323</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160616 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1997 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783034891967</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-0348-9196-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783034899420</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-0348-9942-0</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-0348-9196-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)879623219</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042422323</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kadec, Michail I.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Series in Banach Spaces</subfield><subfield code="b">Conditional and Unconditional Convergence</subfield><subfield code="c">by Mikhail I. Kadets, Vladimir M. Kadets</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Basel</subfield><subfield code="b">Birkhäuser Basel</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VIII, 159 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Operator Theory Advances and Applications</subfield><subfield code="v">94</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problems studied. The phenomenon that a numerical series can change its sum when the order of its terms is changed is one of the most impressive facts encountered in a university analysis course. The present book is devoted precisely to this aspect of the theory of series whose terms are elements of Banach (as well as other topological linear) spaces. The exposition focuses on two complementary problems. The first is to char acterize those series in a given space that remain convergent (and have the same sum) for any rearrangement of their terms; such series are usually called uncon ditionally convergent. The second problem is, when a series converges only for certain rearrangements of its terms (in other words, converges conditionally), to describe its sum range, i.e., the set of sums of all its convergent rearrangements</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvergente Reihe</subfield><subfield code="0">(DE-588)4304017-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Banach-Raum</subfield><subfield code="0">(DE-588)4004402-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Banach-Raum</subfield><subfield code="0">(DE-588)4004402-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Konvergente Reihe</subfield><subfield code="0">(DE-588)4304017-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kadec, Vladimir M.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-0348-9196-7</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027857740</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042422323 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783034891967 9783034899420 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857740 |
| oclc_num | 879623219 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (VIII, 159 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Birkhäuser Basel |
| record_format | marc |
| series2 | Operator Theory Advances and Applications |
| spelling | Kadec, Michail I. Verfasser aut Series in Banach Spaces Conditional and Unconditional Convergence by Mikhail I. Kadets, Vladimir M. Kadets Basel Birkhäuser Basel 1997 1 Online-Ressource (VIII, 159 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory Advances and Applications 94 Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problems studied. The phenomenon that a numerical series can change its sum when the order of its terms is changed is one of the most impressive facts encountered in a university analysis course. The present book is devoted precisely to this aspect of the theory of series whose terms are elements of Banach (as well as other topological linear) spaces. The exposition focuses on two complementary problems. The first is to char acterize those series in a given space that remain convergent (and have the same sum) for any rearrangement of their terms; such series are usually called uncon ditionally convergent. The second problem is, when a series converges only for certain rearrangements of its terms (in other words, converges conditionally), to describe its sum range, i.e., the set of sums of all its convergent rearrangements Mathematics Mathematics, general Mathematik Konvergente Reihe (DE-588)4304017-2 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Konvergente Reihe (DE-588)4304017-2 s 1\p DE-604 Kadec, Vladimir M. Sonstige oth https://doi.org/10.1007/978-3-0348-9196-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kadec, Michail I. Series in Banach Spaces Conditional and Unconditional Convergence Mathematics Mathematics, general Mathematik Konvergente Reihe (DE-588)4304017-2 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4304017-2 (DE-588)4004402-6 |
| title | Series in Banach Spaces Conditional and Unconditional Convergence |
| title_auth | Series in Banach Spaces Conditional and Unconditional Convergence |
| title_exact_search | Series in Banach Spaces Conditional and Unconditional Convergence |
| title_full | Series in Banach Spaces Conditional and Unconditional Convergence by Mikhail I. Kadets, Vladimir M. Kadets |
| title_fullStr | Series in Banach Spaces Conditional and Unconditional Convergence by Mikhail I. Kadets, Vladimir M. Kadets |
| title_full_unstemmed | Series in Banach Spaces Conditional and Unconditional Convergence by Mikhail I. Kadets, Vladimir M. Kadets |
| title_short | Series in Banach Spaces |
| title_sort | series in banach spaces conditional and unconditional convergence |
| title_sub | Conditional and Unconditional Convergence |
| topic | Mathematics Mathematics, general Mathematik Konvergente Reihe (DE-588)4304017-2 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Konvergente Reihe Banach-Raum |
| url | https://doi.org/10.1007/978-3-0348-9196-7 |
| work_keys_str_mv | AT kadecmichaili seriesinbanachspacesconditionalandunconditionalconvergence AT kadecvladimirm seriesinbanachspacesconditionalandunconditionalconvergence |