Some Trapezoidal Vector Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces
نویسندگان
چکیده
منابع مشابه
Some Trapezoidal Vector Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces
and Applied Analysis 3 where ‖ · ‖p p ∈ 1,∞ are the Lebesgue norms, that is, ∥∥f ′∥∞ ess sup s∈ a,b ∣∣f ′ s ∣∣, ∥∥f ′∥∥ p : (∫b a ∣∣f ′ s ∣∣ds)1/p, p ≥ 1. 1.6 The case of convex functions is as follows 4 . Theorem 1.5. Let f : a, b → be a convex function on a, b . Then one has the inequalities 1 8 b − a 2 [ f ′ ( a b 2 ) − f ′ − ( a b 2 )] ≤ f a f b 2 b − a − ∫b
متن کاملEla 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.
متن کاملSome 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.
متن کاملSome 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...
متن کاملSome Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2011
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2011/941286