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The Resource Operator inequalities of the Jensen, Čebyšev and Grüss Type, by Silvestru Sever Dragomir

Operator inequalities of the Jensen, Čebyšev and Grüss Type, by Silvestru Sever Dragomir

Label
Operator inequalities of the Jensen, Čebyšev and Grüss Type
Title
Operator inequalities of the Jensen, Čebyšev and Grüss Type
Statement of responsibility
by Silvestru Sever Dragomir
Creator
Subject
Language
eng
Summary
The main aim of this book is to present recent results concerning inequalities of the Jensen, Čebyšev and Grüss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces.¡ ¡In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The generalized Schwarz's inequality for positive selfadjoint operators as well as some results for the spectrum of this class of operators are presented. This text introduces the reader to the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators as well as the step functions of selfadjoint operators. The spectral decomposition for this class of operators, which play a central role in the rest of the book and its consequences are introduced. At the end of the chapter, some classical operator inequalities are presented as well. Recent new results that deal with different aspects of the famous Jensen operator inequality are explored through the second chapter. These include but are not limited to the operator version of the Dragomir-Ionescu inequality, the Slater type inequalities for operators and its inverses, Jensen's inequality for twice differentiable functions whose second derivatives satisfy some upper and lower bound conditions and Jensen's type inequalities for log-convex functions. Hermite-Hadamard's type inequalities for convex functions and the corresponding results for operator convex functions are also presented. The Čebyšev, (Chebyshev) inequality that compares the integral/discrete mean of the product with the product of the integral/discrete means is famous in the literature devoted to Mathematical Inequalities. The sister inequality due to Grüss which provides error bounds for the magnitude of the difference between the integral mean of the product and the product of the integral means has also attracted much interest since it has been discovered in 1935 with more than 200 papers published so far. The last part of the book is devoted to the operator versions of these famous results for continuous functions of selfadjoint operators on complex Hilbert spaces. Various particular cases of interest and related results are presented as well. This book is intended for use by both researchers in various fields of Linear Operator Theory and Mathematical Inequalities, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Dragomir, Sever Silvestru
Dewey number
515/.724
Index
no index present
LC call number
QA329
LC item number
.D73 2012
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
SpringerBriefs in mathematics,
http://library.link/vocab/subjectName
  • Operator theory
  • Hilbert space
  • Inequalities (Mathematics)
  • Mathematical Concepts
  • Mathematics
  • MATHEMATICS
  • MATHEMATICS
  • Hilbert space
  • Inequalities (Mathematics)
  • Operator theory
Label
Operator inequalities of the Jensen, Čebyšev and Grüss Type, by Silvestru Sever Dragomir
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Functions of selfadjoint operators on Hilbert spaces -- Inequalities of the Jensen type -- Inequalities of the Čebyšev and Grüss type
Control code
761868678
Dimensions
unknown
Extent
1 online resource (xii, 121 pages).
File format
unknown
Form of item
online
Isbn
9781461415213
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)761868678
Label
Operator inequalities of the Jensen, Čebyšev and Grüss Type, by Silvestru Sever Dragomir
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Functions of selfadjoint operators on Hilbert spaces -- Inequalities of the Jensen type -- Inequalities of the Čebyšev and Grüss type
Control code
761868678
Dimensions
unknown
Extent
1 online resource (xii, 121 pages).
File format
unknown
Form of item
online
Isbn
9781461415213
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)761868678

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