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 On Pompeiu Cebysev Type Inequalities for Positive Linear Maps of Selfadjoint Operators in Inner Product Spaces

2018 ◽  
Vol 15 ◽  
pp. 8081-8092
Author(s):  
Mohammad W Alomari
Keyword(s):  
Hilbert Spaces ◽  
Inner Product ◽  
Product Spaces ◽  
Selfadjoint Operators ◽  
Inner Product Spaces ◽  
Linear Maps ◽  
Positive Linear Maps

In this work, generalizations of some inequalities for continuous synchronous (h-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.

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 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 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 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 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 Improving some operator inequalities for positive linear maps

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4333-4340 ◽  
Author(s):  
Chaojun Yang ◽  
Fangyan Lu
Keyword(s):  
Operator Inequalities ◽  
Linear Map ◽  
Linear Maps ◽  
Operator Version ◽  
Positive Linear Maps

Let 0 < mI ? A ? m'I ? M'I ? B ? MI and p ? 1. Then for every positive unital linear map ?, ?2p(A?tB)?(K(h,2)/41p-1(1+Q(t)(log M'm')2) 2p?2p(A#tB) and ?2p(A?tB)?(K(h,2)/41p-1(1+Q(t)(logM'm')2) 2p(?(A)#t ?(B))2p, where t ? [0,1], h = M/m, K(h,2) = (h+1)2/4h, Q(t) = t2/2(1-t/t)2t and Q(0) = Q(1) = 0. Moreover, we give an improvement for the operator version ofWielandt inequality.

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