scholarly journals Landau and Grüss type inequalities for inner product type integral transformers in norm ideals

2013 ◽  
pp. 109-125 ◽  
Author(s):  
Danko R. Jocić ◽  
Đ;orđe Krtinić ◽  
Mohammad Sal Moslehian
Keyword(s):  
Product Type ◽  
Inner Product ◽  
Type Integral ◽  
Grüss Type Inequalities

scholarly journals On properties of inner product type integral transformers

2020 ◽  
Vol 4 (2) ◽  
pp. 160-169
Author(s):  
Benard Okelo ◽  
Keyword(s):  
Quantum Theory ◽  
Product Type ◽  
Inner Product ◽  
Grüss Inequality ◽  
Norm Inequalities ◽  
Unitarily Invariant Norms ◽  
Type Integral

In this paper, we give characterizations of certain properties of inner product type integral transformers. We first consider unitarily invariant norms and operator valued functions. We then give results on norm inequalities for inner product type integral transformers in terms of Landau inequality, Grüss inequality. Lastly, we explore some of the applications in quantum theory.

scholarly journals Some Grüss Type Inequalities for Fréchet Differentiable Mappings

2020 ◽  
Vol 44 (4) ◽  
pp. 571-579
Author(s):  
T. TEIMOURI-AZADBAKHT ◽  
A. G GHAZANFARI
Keyword(s):  
Open Neighborhood ◽  
Continuous Functions ◽  
Inner Product ◽  
C Algebra ◽  
Inner Products ◽  
Fréchet Differentiable ◽  
Grüss Type Inequalities ◽  
Differentiable Mappings

Let X be a Hilbert C∗-module on C∗-algebra A and p ∈ A. We denote by Dp(A,X) the set of all continuous functions f : A → X, which are Fréchet differentiable on a open neighborhood U of p. Then, we introduce some generalized semi-inner products on Dp(A,X), and using them some Grüss type inequalities in semi-inner product C∗-module Dp(A,X) and Dp(A,Xn) are established.

scholarly journals GeneralizednDimensional Ostrowski Type and Grüss Type Inequalities on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Zheng ◽  
Qinghua Feng
Keyword(s):  
Time Scales ◽  
Integral Inequalities ◽  
Discrete Analysis ◽  
Type Integral ◽  
Grüss Type Inequalities

Some new generalizedndimensional Ostrowski type and Grüss type integral inequalities on time scales are established in this paper. The present results unify continuous and discrete analysis, and extend some known results in the literature.

scholarly journals Grüss type inequalities in inner product modules

2005 ◽  
Vol 133 (11) ◽  
pp. 3271-3280 ◽  
Author(s):  
Dijana Ilišević ◽  
Sanja Varošanec
Keyword(s):  
Inner Product ◽  
Grüss Type Inequalities

scholarly journals Norm inequalities for elementary operators and other inner product type integral transformers with the spectra contained in the unit disc

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 197-206 ◽  
Author(s):  
Danko Jocic ◽  
Stefan Milosevic ◽  
Vladimir Djuric
Keyword(s):  
Unit Disc ◽  
Trace Class ◽  
Inner Product ◽  
Bounded Operators ◽  
Shift Operators ◽  
Hilbert Space Operators ◽  
Type Integral ◽  
Normal Operators ◽  
Elementary Operators ◽  
Trace Class Operators

If {At}t?? and {Bt}t?? are weakly*-measurable families of bounded Hilbert space operators such that transformers X ??? At*XAtd?(t) and X ??? Bt*XBtd?(t) on B(H) have their spectra contained in the unit disc, then for all bounded operators X ||?AX?B|| ? ||X-?? At* XBtd?(t)||, (1) where ?A def= s-limr?1(I + ??,n=1 r2n ??...??|At1...Atn|2d?n(t1,...,tn)-1/2 and ?B by analogy. If additionally ??,n=1 ??n |A*t1...A*tn|2d?n(t1,...,tn) and ?,n=1 ??n|B*t1...B*tn|2d?n(t1,...,tn) both represent bounded operators, then for all p,q,s > 1 such that 1/q + 1/s = 2/p and for all Schatten p trace class operators X ||?1-1q,A X ?1-1s,B|| ? ||?-1/q,A*(X-?? At* XBtd?(t))?-1/s,B*||p.(2) If at least one of those families consists of bounded commuting normal operators, then (1) holds for all unitarily invariant Q-norms. Applications to the shift operators are also given.

Grüss-Landau inequalities for elementary operators and inner product type transformers in Q and Q* norm ideals of compact operators

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2447-2455
Author(s):  
Milan Lazarevic
Keyword(s):  
Hilbert Space ◽  
Probability Measure ◽  
Compact Operators ◽  
Product Type ◽  
Inner Product ◽  
Operator Inequality ◽  
Space Operator ◽  
Bounded Operators ◽  
Normal Operators ◽  
Elementary Operators

For a probability measure ? on ? and square integrable (Hilbert space) operator valued functions {A*t}t??, {Bt}t??, we prove Gr?ss-Landau type operator inequality for inner product type transformers |?? AtXBtd?(t)- ?? At d?(t)X ?? Btd?(t)|2? ? ||??AtA*td?(t)- |??A*td?(t)|2||? (?? B*tX*XBtd?(t)- |X?? Btd?(t)|2)?, for all X ? B(H) and for all ? ? [0,1]. Let p ? 2, ? to be a symmetrically norming (s.n.) function, ? (p) to be its p-modification, ? (p)* is a s.n. function adjoint to ?(p) and ||?||?(p)* to be a norm on its associated ideal C?(p)*(H) of compact operators. If X ? C?(p)*(H) and {?n}?n=1 is a sequence in (0,1], such that ??n=1 ?n = 1 and ??n=1 ||?n-1/2 An f||2+||?-1/2n B*nf||2 < +? for some families {An}? n=1 and {Bn}? n=1 of bounded operators on Hilbert space H and for all f ? H, then ||?? n=1 ?-1n AnXBn-?? n=1 AnX ?? n=1 Bn||?(p)* ? ||???n=1 ?-1n |An|2-|??n=1 An|2 X ? ??n=1 ?-1n |B*n|2-|??n=1 B*n|2||?(p)+, if at least one of those operator families consists of mutually commuting normal operators. The related Gr?ss-Landau type ||?||?(p) norm inequalities for inner product type transformers are also provided.

scholarly journals BESSEL- AND GRÜSS-TYPE INEQUALITIES IN INNER PRODUCT MODULES

2007 ◽  
Vol 50 (1) ◽  
pp. 23-36 ◽  
Author(s):  
Senka Banić ◽  
Dijana Ilišević ◽  
Sanja Varošanec
Keyword(s):  
Inner Product ◽  
C Algebra ◽  
Grüss Type Inequalities

AbstractIn this paper we give Bessel- and Grüss-type inequalities in an inner product module over a proper $H^*$-algebra or a $C^*$-algebra.

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