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

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Ela Vector and Operator Trapezoidal Type Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces∗

Some vector and operator generalized trapezoidal inequalities for continuous functions of selfadjoint operators in Hilbert spaces are given. Applications for power and logarithmic functions of operators are provided as well.

Some Reverses of the Jensen Inequality for Functions of Selfadjoint Operators in Hilbert Spaces

Some Slater Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces

Some inequalities of the Slater type for convex functions of selfad-joint operators in Hilbert spaces H under suitable assumptions for the involved operators are given. Amongst others, it is shown that if A is a positive definite operator with Sp (A) ⊂ [m, M ] and f is convex and has a continuous derivative on [m, M ] , then for any x ∈ H with x = 1 the following inequality holds: 0 ≤ f Af ′ (A...

Some Operator Order Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

Various bounds in the operator order for the following operator transform f̃ (A) := 1 2 [f (A)− f ((m + M) 1H −A)] , where A is a selfadjoint operator in the Hilbert space H with the spectrum Sp (A) ⊆ [m,M ] and f : [m,M ] → C is a continuous function on [m,M ] are given. Applications for the power and logaritmic functions are provided as well.