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In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases.…

Functional Analysis · Mathematics 2008-04-09 Peter Balazs

We introduce the notion of a g-atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of g-fusion frames. Also we shall describe the concept of…

Functional Analysis · Mathematics 2024-03-12 Prasenjit Ghosh , T. K. Samanta

A wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a collection, or system, of unitary operators. We will describe the operator-interpolation approach to wavelet theory using the…

Functional Analysis · Mathematics 2007-05-23 David R. Larson

We introduce a new concept of frame operators for Banach spaces we call a Hilbert-Schauder frame operator. This is a hybird between standard frame theory for Hilbert spaces and Schauder frame theory for Banach spaces. Most of our results…

Functional Analysis · Mathematics 2012-06-28 Rui Liu

Operator-valued frames are natural generalization of frames that have been used in quantum computing, packets encoding, etc. In this paper, we focus on developing the theory about operator-valued frames for finite Hilbert spaces. Some…

Functional Analysis · Mathematics 2010-09-28 Bin Meng

Frame theory has been rapidly generalized and various generalizations have been developed. In this paper, we present a brief survey of the frames in Hilbert $C^{\ast}$-modules, including frames, $\ast$-frames, g-frames, $\ast$-g-frames,…

Functional Analysis · Mathematics 2022-12-20 M'hamed Ghiati , Mohammed Mouniane , Mohamed Rossafi

Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…

Functional Analysis · Mathematics 2023-05-18 A. Aguilera , C. Cabrelli , D. Carbajal , V. Paternostro

K-frames are strongly tools for the reconstruction elements from the range of a bounded linear operator K on a separable Hilbert space H. In this paper, we study some properties of K-frames and introduce the K-frame multipliers. We also…

Functional Analysis · Mathematics 2018-07-24 Ali Akbar Arefijamaal , Mitra Shamsabadi

Due to the importance of frame representation by a bounded operator in dynamical sampling, researchers studied the frames of the form $\{T^{i-1} f\}_{i\in \mathbb{N}}$, which $f$ belongs to separable Hilbert space $\mathcal{H}$ and $T\in…

Functional Analysis · Mathematics 2020-05-12 Fatemeh Ghobadzadeh , Yavar Khedmati , Javad Sedghi Moghaddam

In this Work, We introduce the concept of $\ast$-operator frame, which is a generalization of $\ast$-frames in Hilbert pro-$C^{\ast}$-modules, and we establish some results, we also study the tensor product of $\ast$-operator frame for…

Functional Analysis · Mathematics 2021-11-19 Roumaissae Eljazzar , Mohamed Rossafi

In this paper it is investigated how to find a matrix representation of operators on a Hilbert space with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs).…

Functional Analysis · Mathematics 2008-04-09 Peter Balazs

The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H…

General Mathematics · Mathematics 2019-12-09 Samir Al Mohammady , Sid Ahmed Ould Beinane , Sid Ahmed O. Ahmed Mahmoud

Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…

Functional Analysis · Mathematics 2020-10-20 Vladimir Müller , Yuri Tomilov

In this note we investigate the operators associated with frame sequences in a Hilbert space $H$, i.e., the synthesis operator $T:\ell ^{2}(\mathbb{N}) \to H$, the analysis operator $T^{\ast}:H\to $ $% \ell ^{2}(\mathbb{N}) $ and the…

Functional Analysis · Mathematics 2012-05-31 P. Balazs , M. A. El-Gebeily

Operator-valued frames (or g-frames) are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this paper, we give a new formula for operator-valued…

Functional Analysis · Mathematics 2015-04-27 L. Gavruta , P. Gavruta

Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators.…

Functional Analysis · Mathematics 2022-06-28 Fuad Kittaneh , Hamid Reza Moradi , Mohammad Sababheh

We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.

Functional Analysis · Mathematics 2020-12-08 Emma D'Aniello , Martina Maiuriello

Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…

Functional Analysis · Mathematics 2024-03-18 Guillermina Fongi , María Celeste Gonzalez

In this paper, we obtain some new properties of weaving frames and present some conditions under which a family of frames is woven in Hilbert spaces. Some characterizations of weaving frames in terms of operators are given. We also give a…

Functional Analysis · Mathematics 2019-01-08 Dongwei Li

Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded…

Mathematical Physics · Physics 2012-10-12 J-P. Antoine , P. Balazs