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In this paper, we present a general version of operator Bellman inequality. Also, the refinement of inequality due to J. Aujla and F. Silva for the convex functions is given as well. [ABSTRACT FROM AUTHOR]

In this paper we first introduce N̅qΔ − summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrix A to map these sequence spaces on the spaces c, c0 and l∞. Finally, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces. [ABSTRACT FROM AUTHOR]

Let U be a Hilbert A-module and L(U) the set of all adjointable A-linear maps on U. Let K = {Λx ∈ L(U, Vx) : x ∈ X } and L = {Γx ∈ L(U, Vx) : x ∈ X } be two continuous g-frames for U, K is said to be similar with L if there exists an invertible operator J ∈ L(U) such that Γx = ΛxJ, for all x ∈ X . In this paper, we define the concepts of closeness and nearness between two continuous g-frames. In particular, we show that K and L are near, if and only if they are similar. [ABSTRACT FROM AUTHOR]

Let B(H) denote the algebra of all bounded linear operators acting on a complex Hilbert space H. For A;B 2 B(H), define the bimultiplication operator M2;A;B on the class of Hilbert-Schmidt operators by M2;A;B(X) = AXB. In this paper, we show that if B, the adjoint operator of B, is hyponormal, then co(W0(A)W0(B)) W0(M2;A;B); where co stands for the convex hull and W0(:) denotes the maximal numerical range. If in addition, A is hyponormal, we show that co(W0(A)W0(B)) = W0(M2;A;B): [ABSTRACT FROM AUTHOR]

Let B(H) denote the algebra of all bounded linear operators acting on a complex Hilbert space H. For A;B 2 B(H), define the bimultiplication operator M2;A;B on the class of Hilbert-Schmidt operators by M2;A;B(X) = AXB. In this paper, we show that if B, the adjoint operator of B, is hyponormal, then co(W0(A)W0(B)) W0(M2;A;B); where co stands for the convex hull and W0(:) denotes the maximal numerical range. If in addition, A is hyponormal, we show that co(W0(A)W0(B)) = W0(M2;A;B): [ABSTRACT FROM AUTHOR]

In this paper, we give conditions under which the numerical range of a weighted composition operator, acting on a Hilbert space, contains zero as an interior point and we investigate extreme points of the numerical range of an operator acting on an arbitrary Banach space. Also, we give necessary and sufficient conditions under which the numerical range of an operator on some Banach spaces, to be closed. Finally, we characterize the structure of the numerical range of an operatoracting on Banach weighted Hardy spaces. [ABSTRACT FROM AUTHOR]

Let X be a real 2--Banach space. We follow Gunawan, Mashadi, Gemawati, Nursupiamin and Siwaningrum in saying that x is orthogonal to y if there exists a subspace V of X with codimÇV) = 1 such that ||x + Ay, z\\ N ||x, p|| for every z E V and A 6 R. In this aaper, we prove that every linear mapping T: X --> X which preserve orthogonality is a 2--isometry multiplied by a constant. [ABSTRACT FROM AUTHOR]

The matricial ranges of 2 x 2 complex matrices are revisited. Moreover, using the standard block-matrix techniques, we describe matricial ranges of some special non-quadratic higher order matrices. Finally, we obtain the matricial ranges of some specific 3 x 3 matrices. Various examples are given as well. [ABSTRACT FROM AUTHOR]