scholarly journals Trace inequalities of Cassels and Grüss type for operators in Hilbert spaces

2017 ◽  
Vol 9 (1) ◽  
pp. 74-93
Author(s):  
Sever S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Grüss Inequality ◽  
Selfadjoint Operators ◽  
Trace Inequalities

AbstractSome trace inequalities of Cassels type for operators in Hilbert spaces are provided. Applications in connection to Grüss inequality and for convex functions of selfadjoint operators are also given.

scholarly journals Trace inequalities of Shisha-Mond type for operators in Hilbert spaces

2017 ◽  
Vol 4 (1) ◽  
pp. 32-47
Author(s):  
Sever Silvestru Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Grüss Inequality ◽  
Selfadjoint Operators ◽  
Trace Inequalities

Abstract Some trace inequalities of Shisha-Mond type for operators in Hilbert spaces are provided. Applications in connection to Grüss inequality and for convex functions of selfadjoint operators are also given.

scholarly journals Reverse Jensen’s type Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

2016 ◽  
Vol 30 (1) ◽  
pp. 39-62
Author(s):  
Sever S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Selfadjoint Operators ◽  
Trace Inequalities

AbstractSome reverse Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. Applications for some convex functions of interest and reverses of Hölder and Schwarz trace inequalities are also given.

scholarly journals JENSEN’S TYPE TRACE INEQUALITIES FOR CONVEX FUNCTIONS OF SELFADJOINT OPERATORS IN HILBERT SPACES

2017 ◽  
pp. 981
Author(s):  
Sever Silvestru Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Selfadjoint Operators ◽  
Trace Inequalities

Some Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces are provided. Applications for some convex functions of interest are also given.

scholarly journals Operator Popoviciu’s inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces

2019 ◽  
Vol 10 (4) ◽  
pp. 313-324
Author(s):  
Mohammad W. Alomari
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Positive Operators ◽  
Selfadjoint Operators ◽  
Popoviciu’S Inequality ◽  
Linear Maps ◽  
Superquadratic Functions ◽  
Operator Version ◽  
Positive Linear Maps

AbstractIn this work, an operator version of Popoviciu’s inequality for positive operators on Hilbert spaces under positive linear maps for superquadratic functions is proved. Analogously, using the same technique, an operator version of Popoviciu’s inequality for convex functions is obtained. Some other related inequalities are also presented.

scholarly journals Cebysev’s type inequalities and power inequalities for the Berezin number of operators

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2307-2316
Author(s):  
Mubariz Garayev ◽  
Ulaş Yamancı
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Reproducing Kernel ◽  
Type Inequality ◽  
Reproducing Kernel Hilbert Spaces ◽  
Selfadjoint Operators ◽  
Kernel Hilbert Spaces ◽  
Berezin Number

We give operator analogues of some classical inequalities, including Cebysev type inequality for synchronous and convex functions of selfadjoint operators in Reproducing Kernel Hilbert Spaces (RKHSs). We obtain some Berezin number inequalities for the product of operators. Also, we prove the Berezin number inequality for the commutator of two operators.

scholarly journals Some inequalities for convex functions of selfadjoint operators in Hilbert spaces

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 81-92 ◽  
Author(s):  
Sever Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Selfadjoint Operators

Some inequalities for convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are given. Applications for particular cases of interest are also provided.

scholarly journals Berezin number inequality for convex function in reproducing Kernel Hilbert Space

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5711-5717 ◽  
Author(s):  
Ulaş Yamancı ◽  
Mehmet Gürdal ◽  
Mubariz Garayev
Keyword(s):  
Hilbert Space ◽  
Convex Function ◽  
Hilbert Spaces ◽  
Convex Functions ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Reproducing Kernel Hilbert Spaces ◽  
Selfadjoint Operators ◽  
Kernel Hilbert Spaces ◽  
Berezin Number

By using Hardy-Hilbert?s inequality, some power inequalities for the Berezin number of a selfadjoint operators in Reproducing Kernel Hilbert Spaces (RKHSs) with applications for convex functions are given.

Sign in / Sign up

Export Citation Format

Share Document