A necessary and sufficient condition for a class of matrix operators acting from l1 into l2 to be continuous and compact is given in this paper, which answers I. J. Maddox’s open problem. Suppose A = (aij) be an infinite real matrix. It determines a linear operator A from l1 into l2 (1 6 p1, p2 6∞) according to the following raw:

Suppose X and Y are locally compact Hausdorff spaces, E and F are Banach spaces and F is strictly convex. We show that every linear isometry T from C0(X, E) into C0(Y, F) is essentially a weighted composition operator T f (y) = h(y)(f (ϕ(y))).

In this paper we characterize hypercyclic translation operators on $$B_{0}(\mathcal {H})$$ , the space of all compact linear a Hilbert $$\mathcal {H}$$ . Also, give some sufficient condition for related cosine operator function to be chaotic or topologically transitive.

If φ is an analytic function mapping the unit disk D into itself, the composition operator Cφ is the operator on H 2 given by Cφf = f ◦φ. The structure of the composition operator Cφ is usually complex, even if the function φ is fairly simple. In this paper, we consider composition operators whose symbol φ is a linear fractional transformation mapping the disk into itself. That is, we will assu...

where E: D(E) —• S, D(E) C S, is a linear not necessarily bounded operator in a real Hilbert space S with 1 < dim W < °°, W = ketE, and N: S —> S is a continuous nonlinear operator. In terms of the alternative method (see Cesari [1] , [2]), let P: S —> S be the orthogonal projector with range PS = S0 = W = ker E, let St = (I -P)S, and let S1 be also the range of E. Let H: Sx -—• 5'1 denote a li...

This paper studies trace class perturbation of closed linear relations in Hilbert spaces. The concept is introduced by orthogonal projections. Equivalent characterizations compact and block operator matrices are first given terms their elements, separately. By using them, several equivalent sufficient obtained.

Let X,Y be Banach spaces and consider the w′-topology (the dual weak operator topology) on the space (L(X,Y ), ‖.‖) of bounded linear operators from X into X with the uniform operator norm. L ′ (X,Y ) is the space of all T ∈ L(X,Y ) for which there exists a sequence of compact linear operators (Tn) ⊂ K(X,Y ) such that T = w′ − limnTn. Financial support from the National Council for Science and ...

We continue the study of multidimensional operator multipliers initiated in [12]. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and...