Search results for "Compact operator on Hilbert space"

Some results about operators in nested Hilbert spaces

2005

With the use of interpolation methods we obtain some results about the domain of an operator acting on the nested Hilbert space {ℋf}f∈∑ generated by a self-adjoint operatorA and some estimates of the norms of its representatives. Some consequences in the particular case of the scale of Hilbert spaces are discussed.

The Partial Inner Product Space Method: A Quick Overview

2010

Many families of function spaces play a central role in analysis, in particular, in signal processing (e.g., wavelet or Gabor analysis). Typical are spaces, Besov spaces, amalgam spaces, or modulation spaces. In all these cases, the parameter indexing the family measures the behavior (regularity, decay properties) of particular functions or operators. It turns out that all these space families are, or contain, scales or lattices of Banach spaces, which are special cases ofpartial inner product spaces(PIP-spaces). In this context, it is often said that such families should be taken as a whole and operators, bases, and frames on them should be defined globally, for the whole family, instead o…

Some spectral properties for operators acting on Rigged Hilbert spaces

2015

Operators on Rigged Hilbert spaces have been considered from the 80s of the 20th century on as good ones for describing several physical models whose observable set didn’t turn out to be a C∗-algebra.A notion of resolvent set for an operator acting in a rigged Hilbert space \(\mathcal{D}\subset \mathcal{H}\subset \mathcal{D}^{\times }\) is proposed. This set depends on a family of intermediate locally convex spaces living between \(\mathcal{D}\) and \(\mathcal{D}^{\times }\), called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.

Partial Multiplication of Operators in Rigged Hilbert Spaces

2005

The problem of the multiplication of operators acting in rigged Hilbert spaces is considered. This is done, as usual, by constructing certain intermediate spaces through which the product can be factorized. In the special case where the starting space is the set of C∞-vectors of a self-adjoint operator A, a general procedure for constructing a special family of interspaces is given. Their definition closely reminds that of the Bessel potential spaces, to which they reduce when the starting space is the Schwartz space \(\mathcal{S}(\mathbb{R}^n ).\) Some applications are considered.

Intrinsic characterizations of perturbation classes on some Banach spaces

2010

We investigate relationships between inessential operators and improjective operators acting between Banach spaces X and Y, emphasizing the case in which one of the spaces is a C(K) space. We show that they coincide in many cases, but they are different in the case X=Y =C(K 0), where K 0 is a compact space constructed by Koszmider. Mathematics Subject Classification (2000)47A53 KeywordsInessential operators-Improjective operators-Fredholm theory

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.

Multilinear Fourier multipliers related to time–frequency localization

2013

We consider multilinear multipliers associated in a natural way with localization operators. Boundedness and compactness results are obtained. In particular, we get a geometric condition on a subset A⊂R2d which guarantees that, for a fixed synthesis window ψ∈L2(Rd), the family of localization operators Lφ,ψA obtained when the analysis window φ varies on the unit ball of L2(Rd) is a relatively compact set of compact operators.

Representing compact sets of compact operators and of compact range vector measures

1987