Search results for "init"
showing 10 items of 6629 documents
Unbounded derivations and *-automorphisms groups of Banach quasi *-algebras
2018
This paper is devoted to the study of unbounded derivations on Banach quasi *-algebras with a particular emphasis to the case when they are infinitesimal generators of one parameter automorphisms groups. Both of them, derivations and automorphisms are considered in a weak sense; i.e., with the use of a certain families of bounded sesquilinear forms. Conditions for a weak *-derivation to be the generator of a *-automorphisms group are given.
Fredholm operator families ?II
1984
First, we give a characterization of semi-Fredholm operators (i.e. those which are left or right invertible modulo compact operators) on Hausdorff tvs which generalizes the usual one in the context of Banach spaces. Then we consider a class of semi-Fredholm operator families on tvs which include both the "classical" semi-Fredholm operator valued functions on Banach spaces (continuous in the norm sense), and families of the form T + Kn, where Kn is a collectively compact sequence which converges strongly to O. For these families we prove a general stability theorem.
Property (w) for perturbations of polaroid operators
2008
Abstract A bounded linear operator T ∈ L ( X ) acting on a Banach space satisfies property ( w ) , a variant of Weyl’s theorem, if the complement in the approximate point spectrum σ a ( T ) of the Weyl essential approximate-point spectrum σ wa ( T ) is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this note, we study the stability of property ( w ) for a polaroid operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with T.
Operators which have a closed quasi-nilpotent part
2002
We find several conditions for the quasi-nilpotent part of a bounded operator acting on a Banach space to be closed. Most of these conditions are established for semi-Fredholm operators or, more generally, for operators which admit a generalized Kato decomposition. For these operators the property of having a closed quasi-nilpotent part is related to the so-called single valued extension property.
Evolution semigroups and time operators on Banach spaces
2010
AbstractWe present new general methods to obtain shift representation of evolution semigroups defined on Banach spaces. We introduce the notion of time operator associated with a generalized shift on a Banach space and give some conditions under which time operators can be defined on an arbitrary Banach space. We also tackle the problem of scaling of time operators and obtain a general result about the existence of time operators on Banach spaces satisfying some geometric conditions. The last part of the paper contains some examples of explicit constructions of time operators on function spaces.
Classical operators on weighted Banach spaces of entire functions
2013
We study the operators of differentiation and of integration and the Hardy operator on weighted Banach spaces of entire functions. We estimate the norm of the operators, study the spectrum, and analyze when they are surjective, power bounded, hypercyclic, and (uniformly) mean ergodic.
Spectra and essential spectral radii of composition operators on weighted Banach spaces of analytic functions
2008
AbstractWe determine the spectra of composition operators acting on weighted Banach spaces Hv∞ of analytic functions on the unit disc defined for a radial weight v, when the symbol of the operator has a fixed point in the open unit disc. We also investigate in this case the growth rate of the Koenigs eigenfunction and its relation with the essential spectral radius of the composition operator.
Operator martingale decomposition and the Radon-Nikodym property in Banach spaces
2010
Abstract We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon–Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney–Schaefer l-tensor product E ⊗ ˜ l Y , where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon–Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on E ⊗ ˜ l Y . Secondly, we derive a Riesz decomposition for uniform …
The Average State Complexity of the Star of a Finite Set of Words Is Linear
2008
We prove that, for the uniform distribution over all sets Xof m(that is a fixed integer) non-empty words whose sum of lengths is n, $\mathcal{D}_X$, one of the usual deterministic automata recognizing X*, has on average $\mathcal{O}(n)$ states and that the average state complexity of X*is i¾?(n). We also show that the average time complexity of the computation of the automaton $\mathcal{D}_X$ is $\mathcal{O}(n\log n)$, when the alphabet is of size at least three.
Bloch functions on the unit ball of an infinite dimensional Hilbert space
2015
The Bloch space has been studied on the open unit disk of C and some ho- mogeneous domains of C n . We dene Bloch functions on the open unit ball of a Hilbert space E and prove that the corresponding space B(BE) is invariant under composition with the automorphisms of the ball, leading to a norm that- modulo the constant functions - is automorphism invariant as well. All bounded analytic functions on BE are also Bloch functions. ones, resulting the fact that if for a given n; the restrictions of the function to the n-dimensional subspaces have their Bloch norms uniformly bounded, then the function is a Bloch one and conversely. We also introduce an equivalent norm forB(BE) obtained by repla…