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

S. Mecheri (2007)

Czechoslovak Mathematical Journal

Let ℋ be a separable infinite dimensional complex Hilbert space, and let ℒ ( ℋ ) denote the algebra of all bounded linear operators on ℋ into itself. Let A = ( A 1 , A 2 , ⋯ , A n ) , B = ( B 1 , B 2 , ⋯ , B n ) be n -tuples of operators in ℒ ( ℋ ) ; we define the elementary operators Δ A , B ℒ ( ℋ ) ↦ ℒ ( ℋ ) 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 ∈ ℒ ( ℋ ) satisfying Putnam-Fuglede’s property, i.e, the class of pairs of operators A , B ∈ ℒ ( ℋ ) 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 ( ℋ ) (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.

Currently displaying 381 – 400 of 11160