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
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The item Operator inequalities of the Jensen, Čebyšev and Grüss Type, by Silvestru Sever Dragomir represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Operator inequalities of the Jensen, Čebyšev and Grüss Type, by Silvestru Sever Dragomir represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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 DragomirIonescu 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 logconvex functions. HermiteHadamard'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
 Language
 eng
 Extent
 1 online resource (xii, 121 pages).
 Contents

 Functions of selfadjoint operators on Hilbert spaces
 Inequalities of the Jensen type
 Inequalities of the Čebyšev and Grüss type
 Isbn
 9781461415213
 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
 Subject

 Distribution (Probability theory)
 Hilbert space
 Hilbert space
 Hilbert space
 Inequalities (Mathematics)
 Inequalities (Mathematics)
 Inequalities (Mathematics)
 MATHEMATICS  Calculus
 MATHEMATICS  Mathematical Analysis
 Mathematical Concepts
 Mathematics
 Mathematics  methods
 Operator theory
 Operator theory
 Operator theory
 Partial Differential Equations
 Probability Theory and Stochastic Processes
 Differential equations, partial
 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 DragomirIonescu 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 logconvex functions. HermiteHadamard'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
 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
 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
 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
Subject
 Distribution (Probability theory)
 Hilbert space
 Hilbert space
 Hilbert space
 Inequalities (Mathematics)
 Inequalities (Mathematics)
 Inequalities (Mathematics)
 MATHEMATICS  Calculus
 MATHEMATICS  Mathematical Analysis
 Mathematical Concepts
 Mathematics
 Mathematics  methods
 Operator theory
 Operator theory
 Operator theory
 Partial Differential Equations
 Probability Theory and Stochastic Processes
 Differential equations, partial
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