Some inequalities of Cauchy-Bunyakovsky-Schwarz type for sequences of bounded linear operators in Hilbert spaces and some applications are given.

In this note we describe the dual and the completion of the space of finite linear combinations of (p,∞)-atoms, 0 < p ≤ 1. As an application, we show an extension result for operators uniformly bounded on (p,∞)-atoms, 0 < p < 1, whose analogue for p = 1 is known to be false. Let 0 < p < 1 and let T be a linear operator defined on the space of finite linear combinations of (p,∞)-atoms, 0 < p < 1...

These notes are largely concerned with the strong and weak operator topologies on spaces of bounded linear operators, especially on Hilbert spaces, and related matters.

Here we look at strong and weak operator topologies on spaces of bounded linear mappings, and convergence of sequences of operators with respect to these topologies in particular.

The largest class of linear MIMO convolution operators that preserves positivity of repeated MIMO, incrementally positive, norm-bounded, memoryless nonlinearities is obtained.

In this note we investigate generalized projections in Banach algebras. Our results generalize results obtained for bounded linear operators on Hilbert spaces.

Srivastava and Gupta proposed in 2003 a general family of linear positive operators which include several well known operators as its special cases and investigated the rate of convergence of these operators for functions of bounded variation by using the decomposition techniques. Subsequently, researchers proposed several modifications of these operators and studied their various approximation...

Let B(X ) be the algebra of all bounded linear operators on a complex Banach space X and let I(X ) be the set of non-zero idempotent operators in B(X ). A surjective map φ : B(X ) → B(X ) preserves nonzero idempotency of the Jordan products of two operators if for every pair A, B ∈ B(X ), the relation AB + BA ∈ I(X ) implies φ(A)φ(B) + φ(B)φ(A) ∈ I(X ). In this paper, the structures of linear s...

Let B(X ) be the algebra of all bounded linear operators on a complex Banach space X and let I(X ) be the set of non-zero idempotent operators in B(X ). A surjective map φ : B(X ) → B(X ) preserves nonzero idempotency of the Jordan products of two operators if for every pair A, B ∈ B(X ), the relation AB +BA ∈ I(X ) implies φ(A)φ(B)+φ(B)φ(A) ∈ I(X ). In this paper, the structures of linear surj...

In this paper, we derive certain algebraic properties of Toeplitz and Hankel operators defined on the vector-valued Bergman spaces L2,C n a (D), where D is the open unit disk in C and n ≥ 1. We show that the set of all Toeplitz operators TΦ,Φ ∈ LMn(D) is strongly dense in the set of all bounded linear operators L(L2,Cn a (D)) and characterize all finite rank little Hankel operators.