Ideal-triangularizability of upward directed sets of positive operators.
Integral representation of the -th derivative in de Branges-Rovnyak spaces and the norm convergence of its reproducing kernel
In this paper, we give an integral representation for the boundary values of derivatives of functions of the de Branges–Rovnyak spaces , where is in the unit ball of . In particular, we generalize a result of Ahern–Clark obtained for functions of the model spaces , where is an inner function. Using hypergeometric series, we obtain a nontrivial formula of combinatorics for sums of binomial coefficients. Then we apply this formula to show the norm convergence of reproducing kernel of evaluation...
Invariant Subspaces and Spectral Conditions on Operator Semigroups
Invariant subspaces and spectral mapping theorems
We discuss some results and problems connected with estimation of spectra of operators (or elements of general Banach algebras) which are expressed as polynomials in several operators, noncommuting but satisfying weaker conditions of commutativity type (for example, generating a nilpotent Lie algebra). These results have applications in the theory of invariant subspaces; in fact, such applications were the motivation for consideration of spectral problems. More or less detailed proofs are given...
Invariant subspaces for operators in a general II1-factor
Let ℳ be a von Neumann factor of type II1 with a normalized trace τ. In 1983 L. G. Brown showed that to every operator T∈ℳ one can in a natural way associate a spectral distribution measure μ T (now called the Brown measure of T), which is a probability measure in ℂ with support in the spectrum σ(T) of T. In this paper it is shown that for every T∈ℳ and every Borel set B in ℂ, there is a unique closed T-invariant subspace affiliated with ℳ, such that the Brown measure of is concentrated on B...
Invariant subspaces for polynomially compact almost superdiagonal operators on .
Invariant subspaces for some operators on locally convex spaces
The invariant subspace problem for some operators and some operator algebras acting on a locally convex space is studied.
Invariant Subspaces of Compact Elements in C*-Algebras.
Invariant subspaces of L... and H... .
Invariant subspaces of the Dirichlet shift.
Invariant subspaces of under the action of biconjugates
We study conditions on an infinite dimensional separable Banach space implying that is the only non-trivial invariant subspace of under the action of the algebra of biconjugates of bounded operators on : . Such a space is called simple. We characterize simple spaces among spaces which contain an isomorphic copy of , and show in particular that any space which does not contain and has property (u) of Pelczynski is simple.
Invariant subspaces on multiply connected domains.
The lattice of invariant subspaces of several Banach spaces of analytic functions on the unit disk, for example the Bergman spaces and the Dirichlet spaces, have been studied recently. A natural question is to what extent these investigations carry over to analogously defined spaces on an annulus. We consider this question in the context of general Banach spaces of analytic functions on finitely connected domains Ω. The main result reads as follows: Assume that B is a Banach space of analytic functions...
Invariant subspaces on open Riemann surfaces. II
We considerably improve our earlier results [Ann. Inst. Fourier, 24-4 (1974] concerning Cauchy-Read’s theorems, convergence of Green lines, and the structure of invariant subspaces for a class of hyperbolic Riemann surfaces.
Isometric parts of operators and the critical exponent