The calculus of operator functions and operator convexity:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Warszawa
Polska Akad. Nauk, Inst. Matematyczny
2000
|
| Series: | Dissertationes mathematicae
390 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 48 S. |
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Record in the Search Index
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| adam_text |
POLSKA AKADEMIA NAUK, INSTYTUT MATEMATYCZNY D I S S E R T A T I O N E S
M A T H E M A T I C A E (ROZPRAWY MATEMATYCZNE) KOMITET REDAKCYJNY
ANDRZEJ BIALYNICKI-BIRULA, BOGDAN BOJARSKI, ZBIGNIEW CIESIELSKI, LUDOMIR
NEWELSKI, ZBIGNIEW SEMADENI, JERZY ZABCZYK REDAKTOR, WIESLAW ZELAZKO
ZAST^PCA REDAKTORA CCCXC A. L. BROWN AND H. L. VASUDEVA THE CALCULUS OF
OPERATOR FUNCTIONS AND OPERATOR CONVEXITY SUB GOTTINGEN 7 212 248 715
WARSZAWA 2000 CONTENTS 1. INTRODUCTION 5 I. THE CALCULUS 7 2. OPERATOR
FUNCTIONS OF ONE VARIABLE 7 3. OPERATOR MONOTONICITY AND CONVEXITY 13 4.
OPERATOR FUNCTIONS OF TWO VARIABLES 17 II. OPERATOR CONVEX FUNCTIONS OF
TWO VARIABLES 22 5. PRELIMINARIES 22 6. SEPARATELY EXTREMAL FUNCTIONS OF
TWO VARIABLES 24 7. A CHARACTERISATION OF FUNCTIONS IN F(A, /3,E) 33 8.
THE FACES F(A, 0, E) OF OC 2 39 REFERENCES 47 2000 MATHEMATICS SUBJECT
CLASSIFICATION: 47A60, 47A63, 52A07, 26B25, 26B12. THE FIRST NAMED
AUTHOR GRATEFULLY ACKNOWLEDGES THE SUPPORT OF THE NATIONAL BOARD FOR
HIGHER MATHEMATICS OF INDIA DURING THE PERIODS MARCH-SEPTEMBER 1993 AND
NOVEMBER 1996-JA- NUARY 1998. '' RECEIVED 21.10.1998; REVISED 20.4.2000.
ABSTRACT THE PAPER IS CONCERNED WITH THE FRECHET DIFFERENTIABILITY AND
OPERATOR CONVEXITY OF THE OPERATOR FUNCTIONS ON SETS OF SELF-ADJOINT
OPERATORS ON FINITE-DIMENSIONAL INNER PRODUCT SPACES WHICH ARE
ASSOCIATED WITH REAL-VALUED FUNCTIONS OF ONE OR TWO VARIABLES. IN PART I
IT IS SHOWN THAT IF A REAL- VALUED FUNCTION IS L TIMES CONTINUOUSLY
DIFFERENTIABLE THEN THE ASSOCIATED OPERATOR FUNCTIONS ARE L TIMES
PRECHET DIFFERENTIABLE WITH CONTINUOUS FRECHET DERIVATIVES. IT IS SHOWN
THAT THE OPERATOR FUNCTIONS CORRESPONDING TO A REAL-VALUED FUNCTION /
CAN BE EXPRESSED ALGEBRAICALLY IN TERMS OF ITS FIRST PRECHET
DERIVATIVES. THERE ARE THEN THE NATURAL DIFFERENTIAL CONDITIONS FOR
OPERATOR MONOTONICITY AND CONVEXITY AND THE LATTER IS USED IN PART II
WHICH IS CONCERNED WITH OPERATOR CONVEX FUNCTIONS OF TWO VARIABLES. THE
SET QCI OF OPERATOR CONVEX FUNCTIONS ON (*1,1) 2 IS A CONVEX CONE. A
THREE-PARAMETER FAMILY OF FACES F(A, /3, E), OF DIMENSION 3 (THE TRIVIAL
CASE), 4, 6, 7 OR 8, OF OCI IS IDENTIFIED AND INVESTIGATED. |
| any_adam_object | 1 |
| author | Brown, Aldric L. Vasudeva, Harkrishan L. |
| author_facet | Brown, Aldric L. Vasudeva, Harkrishan L. |
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| dewey-full | 515.724 |
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| discipline | Mathematik |
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| indexdate | 2025-02-25T11:04:56Z |
| institution | BVB |
| language | English |
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| physical | 48 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Polska Akad. Nauk, Inst. Matematyczny |
| record_format | marc |
| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Brown, Aldric L. Verfasser aut The calculus of operator functions and operator convexity A. L. Brown and H. L. Vasudeva Warszawa Polska Akad. Nauk, Inst. Matematyczny 2000 48 S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 390 Convex functions Monotone operators Operator theory Operator-valued functions Vasudeva, Harkrishan L. Verfasser aut Dissertationes mathematicae 390 (DE-604)BV000003039 390 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009256919&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brown, Aldric L. Vasudeva, Harkrishan L. The calculus of operator functions and operator convexity Dissertationes mathematicae Convex functions Monotone operators Operator theory Operator-valued functions |
| title | The calculus of operator functions and operator convexity |
| title_auth | The calculus of operator functions and operator convexity |
| title_exact_search | The calculus of operator functions and operator convexity |
| title_full | The calculus of operator functions and operator convexity A. L. Brown and H. L. Vasudeva |
| title_fullStr | The calculus of operator functions and operator convexity A. L. Brown and H. L. Vasudeva |
| title_full_unstemmed | The calculus of operator functions and operator convexity A. L. Brown and H. L. Vasudeva |
| title_short | The calculus of operator functions and operator convexity |
| title_sort | the calculus of operator functions and operator convexity |
| topic | Convex functions Monotone operators Operator theory Operator-valued functions |
| topic_facet | Convex functions Monotone operators Operator theory Operator-valued functions |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009256919&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003039 |
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