We obtain several characterizations for the classes of Riesz and inessential operators, and apply them to extend the family of Banach spaces for which the essential incomparability class is known, solving partially a problem posed in [6].
The space of inessential bounded linear operators from one Banach space into another is introduced. This space, , is a subspace of which generalizes Kleinecke’s ideal of inessential operators. For certain subspaces of , it is shown that when has a generalized inverse modulo , then there exists a projection such that has a generalized inverse and .
In this paper we prove some properties of the lower s-numbers and derive asymptotic formulae for the jumps in the semi-Fredholm domain of a bounded linear operator on a Banach space.
Antilinear operators on a complex Hilbert space arise in various contexts in mathematical physics. In this paper, an analogue of the Weyl-von Neumann theorem for antilinear self-adjoint operators is proved, i.e. that an antilinear self-adjoint operator is the sum of a diagonalizable operator and of a compact operator with arbitrarily small Schatten p-norm. On the way, we discuss conjugations and their properties. A spectral integral representation for antilinear self-adjoint operators is constructed....
Let A be a closed linear operator acting in a separable Hilbert space. Denote by co(A) the closed convex hull of the spectrum of A. An estimate for the norm of f(A) is obtained under the following conditions: f is a holomorphic function in a neighbourhood of co(A), and for some integer p the operator is Hilbert-Schmidt. The estimate improves one by I. Gelfand and G. Shilov.
We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H₀(λI - T) as λ belongs to certain sets of ℂ. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators.
An operator T acting on a Banach space X has property (gw) if , where is the approximate point spectrum of T, is the upper semi-B-Weyl spectrum of T and E(T) is the set of all isolated eigenvalues of T. We introduce and study two new spectral properties (v) and (gv) in connection with Weyl type theorems. Among other results, we show that T satisfies (gv) if and only if T satisfies (gw) and .