Related papers: Dual pair and Approximate dual for continuous fram…
The concepts of controlled frames and it's dual in n-Hilbert spaces and their tensor products have been introduced and then some of their characterizations are given. We further study the relationship between controlled frame and bounded…
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).…
Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…
The duality of uniform approximation property for Banach spaces is well known. In this note, we establish, under the assumption of local reflexivity, the duality of uniform approximation property in the category of operator spaces.
In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator…
Famous Naimark-Han-Larson dilation theorem for frames in Hilbert spaces states that every frame for a separable Hilbert space $\mathcal{H}$ is image of a Riesz basis under an orthogonal projection from a separable Hilbert space…
We compare the concept of triplet of closely embedded Hilbert spaces with that of generalised triplet of Hilbert spaces in the sense of Berezanskii by showing when they coincide, when they are different, and when starting from one of them…
In this work we prove analogues of Bessel inequality and Riesz-Fisher theorem in Hilbert spaces with respect to sequences. We apply our generalized Bessel inequality to the Hilbert spaces associated with the Normal, Beta, Gamma and certain…
In~\cite{holub1994bases} Holub introduced the concept of near-Riesz bases, as frames that can be considered Riesz bases for computational purposes or that exhibit certain desirable properties of Riesz bases. In this paper, we introduce a…
The notions of Bessel sequence, Riesz-Fischer sequence and Riesz basis are generalized to a rigged Hilbert space $\D[t] \subset \H \subset \D^\times[t^\times]$. A Riesz-like basis, in particular, is obtained by considering a sequence…
In this paper, we introduce the concept of $K$-fusion frames and propose the duality for such frames. The relation between the local frames of $K$-fusion frames with their dual is studied. The elements from the range of a bounded linear…
We provide a summary of the continuity properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator…
With the aim of representing subsets of Banach spaces as an infinite series using Lipschitz functions, we study a variant of metric frames which we call Lipschitz p-approximate Schauder frames (Lipschitz p-ASFs). We characterize Lipschitz…
In this paper, we introduce and study the frames in separable quaternionic Hilbert spaces. Results on the existence of frames in quaternionic Hilbert spaces have been given. Also, a characterization of frame in quaternionic Hilbert spaces…
We study finite systems of subspaces of a complex Hilbert space such that each pair of subspaces satisfies a certain condition as described in the following. For each subspace excepting the first one an angle between this subspace and the…
Extensions of dual definite subspaces to dual maximal definite ones are described. The concepts of dual quasi maximal subspaces and quasi basis are introduced and studied. The obtained results are applied to the classification of…
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…
Several important algorithms for machine learning and data analysis use pairwise distances as input. On Riemannian manifolds these distances may be prohibitively costly to compute, in particular for large datasets. To tackle this problem,…
There are two notions of approximate Birkhoff-James orthogonality in a normed space. We characterize both the notions of approximate Birkhoff-James orthogonality in the space of bounded linear operators defined on a normed space. A complete…
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation…