SOME INEQUALITIES OF JENSEN TYPE FOR ARG-SQUARE CONVEX FUNCTIONS OF UNITARY OPERATORS IN HILBERT SPACES

2014 ◽  
Vol 90 (1) ◽  
pp. 65-73
Author(s):  
S. S. DRAGOMIR
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Unitary Operators

AbstractSome inequalities of Jensen type for Arg-square-convex functions of unitary operators in Hilbert spaces are 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 Mutually unbiased unitary bases of operators on d-dimensional hilbert space

2020 ◽  
Vol 18 (01) ◽  
pp. 1941026 ◽  
Author(s):  
Rinie N. M. Nasir ◽  
Jesni Shamsul Shaari ◽  
Stefano Mancini
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Unitary Operator ◽  
Dimensional Subspace ◽  
Mutually Unbiased Bases ◽  
Unitary Operators ◽  
Dimension Formula ◽  
Dimensional Hilbert Space ◽  
Prime Dimension

Analogous to the notion of mutually unbiased bases for Hilbert spaces, we consider mutually unbiased unitary bases (MUUBs) for the space of operators, [Formula: see text], acting on such Hilbert spaces. The notion of MUUB reflects the equiprobable guesses of unitary operators in one basis of [Formula: see text] when estimating a unitary operator in another. Though, for prime dimension [Formula: see text], the maximal number of MUUBs is known to be [Formula: see text], there is no known recipe for constructing them, assuming they exist. However, one can always construct a minimum of three MUUBs, and the maximal number is approached for very large values of [Formula: see text]. MUUBs can also exist for some [Formula: see text]-dimensional subspace of [Formula: see text] with the maximal number being [Formula: see text].

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 Absolute Quantum Theory (after Chang, Lewis, Minic and Takeuchi), and a Road to Quantum Deletion

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 174
Author(s):  
Koen Thas
Keyword(s):  
Quantum Theory ◽  
Finite Fields ◽  
Hilbert Spaces ◽  
Inner Product ◽  
Unitary Operators ◽  
Evolution Operators ◽  
Quantum Theories ◽  
Classical Quantum ◽  
Absolute Quantum ◽  
Made In

In a recent paper, Chang et al. have proposed studying “quantum F u n ”: the q ↦ 1 limit of modal quantum theories over finite fields F q , motivated by the fact that such limit theories can be naturally interpreted in classical quantum theory. In this letter, we first make a number of rectifications of statements made in that paper. For instance, we show that quantum theory over F 1 does have a natural analogon of an inner product, and so orthogonality is a well-defined notion, contrary to what was claimed in Chang et al. Starting from that formalism, we introduce time evolution operators and observables in quantum F u n , and we determine the corresponding unitary group. Next, we obtain a typical no-cloning result in the general realm of quantum F u n . Finally, we obtain a no-deletion result as well. Remarkably, we show that we can perform quantum deletion by almost unitary operators, with a probability tending to 1. Although we develop the construction in quantum F u n , it is also valid in any other quantum theory (and thus also in classical quantum theory in complex Hilbert spaces).

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.

Trapezoid type inequalities for complex functions defined on the unit circle with applications for unitary operators in Hilbert spaces

2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Sever S. Dragomir
Keyword(s):  
Unit Circle ◽  
Hilbert Spaces ◽  
Stieltjes Integral ◽  
Unitary Operators ◽  
Complex Functions ◽  
Continuous Complex ◽  
Complex Valued

AbstractSome trapezoid type inequalities for the Riemann–Stieltjes integral of continuous complex-valued integrands defined on the complex unit circle

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