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A new characterization of Anderson’s inequality in C 1 -classes

S. Mecheri (2007)

Czechoslovak Mathematical Journal

Let be a separable infinite dimensional complex Hilbert space, and let ( ) denote the algebra of all bounded linear operators on into itself. Let A = ( A 1 , A 2 , , A n ) , B = ( B 1 , B 2 , , B n ) be n -tuples of operators in ( ) ; we define the elementary operators Δ A , B ( ) ( ) by Δ A , B ( X ) = i = 1 n A i X B i - X . In this paper, we characterize the class of pairs of operators A , B ( ) satisfying Putnam-Fuglede’s property, i.e, the class of pairs of operators A , B ( ) such that i = 1 n B i T A i = T implies i = 1 n A i * T B i * = T for all T 𝒞 1 ( ) (trace class operators). The main result is the equivalence between this property and the fact that...

A new class of nonexpansive type mappings and fixed points

Ljubomir B. Ćirić (1999)

Czechoslovak Mathematical Journal

In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.

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