Related papers: A Systematic Study of Frame Sequence Operators and…

Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence (called the symbol) and…

We characterize the normal operators $A$ on $\ell^2$ and the elements $a^i \in \ell^2$, with $1\le i\le m$, such that the sequence $$\{ A^n a^1 , \ldots , A^n a^m \}_{n\ge 0}$$ is a frame. The characterization makes strong use of the…

The construction of frames for a Hilbert space H can be equated to the decomposition of the frame operator as a sum of positive operators having rank one. This realization provides a different approach to questions regarding frames with…

We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…

In this paper, we introduce a new type of parallelism for bounded linear operators on a Hilbert space $\big(\mathscr{H}, \langle \cdot ,\cdot \rangle\big)$ based on numerical radius. More precisely, we consider operators $T$ and $S$ which…

Frames in a separable quaternionic Hilbert space were introduced and studied in [17] to have more applications. In this paper, we extend the study of frames in quaternionic Hilbert spaces and introduce different types of duals of a frame in…

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…

Recently, fusion frames and frames for operators were considered as generalizations of frames in Hilbert spaces. In this paper, we generalize some of the known results in frame theory to fusion frames related to a linear bounded operator K…

This paper is a sequel to [6]. In that paper we transferred the discussions in [1] and [13] concerning almost invariant half-spaces for operators on complex Banach spaces to the context of operators on Hilbert space, and we gave easier…

This paper considers paired operators in the context of the Lebesgue Hilbert space $L^2$ on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are…

The purpose of this note is to answer a question A. E. Nussbaum formulated in 1964 about the possible equivalence between weak measurability of a family of densely defined, closed operators T(t), t real, in a separable complex Hilbert space…

We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related modular operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea…

We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm…

Using the notions of frame transform and of square integrable projective representation of a locally compact group $G$, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier…

Motivated by the study of frame properties arising from iterates of linear operators, it was previously established that the multiplication operator $T_{\phi}x(t) = \phi(t)x(t)$ cannot generate a frame in $L^2(a,b)$ (Results Math, 2019). In…

We suppose that $G$ is a locally compact abelian group, $Y$ is a measure space, and $H$ is a reproducing kernel Hilbert space on $G\times Y$ such that $H$ is naturally embedded into $L^2(G\times Y)$ and it is invariant under the…

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…

This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…

The numerical range of a bounded linear operator on a complex Banach space need not be convex unlike that on a Hilbert space. The aim of this paper is to study operators $T$ on $ \ell^2_p $ for which the numerical range is convex. We also…

Applying the techniques resulting the existence of almost invariant half-spaces, similarity models $\wh T$ can be given for upper triangular operator-matrices $T= \left[\begin{matrix}A&C\\ 0&B\end{matrix}\right]$. The model $\wh T$ is also…