Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Characterizations and representations of Hilbert-Schmidt frames in Hilbert spaces
View through CrossRef
Hilbert-Schmidt frame(HS-frame) is essentially an operator-valued frame,
it is more general than g-frames, and thus, covers some generalizations
of frames. This paper addresses the Hilbert-Schmidt frames theory for
Hilbert spaces. We first introduce the notion of HS-preframe operator,
and characterize the HS-frames, Parseval HS-frames, HS-Riesz bases,
HS-orthonormal bases and dual HS-frames in terms of HS-preframe
operators. In particular, we characterize the dual HS-frames in a
constructive way, that is, the algebraic formulae for all dual HS-frames
of a given HS-frame are given. Then we discuss the sum of HS-frames
through the properties of HS-preframe operators. Finally, we present the
representations of HS-frames in terms of linear combinations of simpler
ones such as HS-orthonormal bases, HS-Riesz bases and Parseval
HS-frames, especially an HS-frame can be represented as a linear
combination of two HS-orthonormal bases if and only if it is an HS-Riesz
basis.
Title: Characterizations and representations of Hilbert-Schmidt frames in Hilbert spaces
Description:
Hilbert-Schmidt frame(HS-frame) is essentially an operator-valued frame,
it is more general than g-frames, and thus, covers some generalizations
of frames.
This paper addresses the Hilbert-Schmidt frames theory for
Hilbert spaces.
We first introduce the notion of HS-preframe operator,
and characterize the HS-frames, Parseval HS-frames, HS-Riesz bases,
HS-orthonormal bases and dual HS-frames in terms of HS-preframe
operators.
In particular, we characterize the dual HS-frames in a
constructive way, that is, the algebraic formulae for all dual HS-frames
of a given HS-frame are given.
Then we discuss the sum of HS-frames
through the properties of HS-preframe operators.
Finally, we present the
representations of HS-frames in terms of linear combinations of simpler
ones such as HS-orthonormal bases, HS-Riesz bases and Parseval
HS-frames, especially an HS-frame can be represented as a linear
combination of two HS-orthonormal bases if and only if it is an HS-Riesz
basis.
Related Results
Achievements on Matrix Hilbert spaces and reproducing kernel matrix Hilbert spaces
Achievements on Matrix Hilbert spaces and reproducing kernel matrix Hilbert spaces
Abstract
Hilbert space is a very powerfull mathematical tool that has proven to be incredibily useful in a wide range of applications. Matrix Hilebrt space is a new fram...
Hilbert bundles with ends
Hilbert bundles with ends
Given a countable metric space, we can consider its end. Then a basis of a Hilbert space indexed by the metric space defines an end of the Hilbert space, which is a new notion and ...
Meta-Representations as Representations of Processes
Meta-Representations as Representations of Processes
In this study, we explore how the notion of meta-representations in Higher-Order Theories (HOT) of consciousness can be implemented in computational models. HOT suggests that consc...
Bernhard Schmidt and the Schmidt Telescope for Mapping the Sky
Bernhard Schmidt and the Schmidt Telescope for Mapping the Sky
Abstract
Bernhard Voldemar Schmidt (1879-1935) was born in Estonia. He ran an optical workshop in Mittweida, Saxonia, between 1901 and 1927. Astronomers appreciated...
Representation and duality for Hilbert algebras
Representation and duality for Hilbert algebras
Abstract
In this paper we introduce a special kind of ordered topological spaces, called Hilbert spaces. We prove that the category of Hilbert algebras with semi-hom...
FRAMES OF SOCIAL REPRESENTATIONS: STRUCTURE AND FORMATION FEATURES
FRAMES OF SOCIAL REPRESENTATIONS: STRUCTURE AND FORMATION FEATURES
Purpose of the study: The purpose of this article is to determine the features of the framing process, taking into account the methodological basis of the theory of frames. Methodo...
Partial frames, their free frames and their congruence frames
Partial frames, their free frames and their congruence frames
The context of this work is that of partial frames; these are meet-semilattices where not all subsets need have joins. A selection function, S, specifies, for all meet-semilattices...
*-Controlled frames in Hilbert C*-modules
*-Controlled frames in Hilbert C*-modules
The main purpose of this paper is to introduce the notion of *-T-controlled frames in Hilbert [Formula: see text]-modules. We present some results of frames in the view of *-T-cont...