Generalized atomic subspaces for operators in Hilbert spaces

Prasenjit Ghosh; T. K. Samanta

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Generalized atomic subspaces for operators in Hilbert spaces

Prasenjit Ghosh, T. K. Samanta

Functional Analysis · Submitted 3 Feb 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.04 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.04 · mentions code or data availability 0.02.

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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 frame operator for a pair of g-fusion Bessel sequences and some of their properties.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	contribution 1.00	0.95	0.45	asserted 1.00
s1	Also we shall describe the concept of frame operator for a pair of g-fusion Bessel sequences and some of their properties.	contribution 1.00	0.74	0.09	asserted 0.98

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The paper

Original abstract

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 frame operator for a pair of g-fusion Bessel sequences and some of their properties.

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2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 2 papers

Samanta [ref] . $K$-frame is also presented to reconstruct elements from the range of a bounded linear operator $K$ in a separable Hilbert space and it is a generalization of the ordinary frames.

Atomic systems in n-Hilbert spaces and their tensor products · Introduction · 0.91
Samanta [ref] and they were also presented the stability of dual $g$-fusion frames in Hilbert spaces in [ref] .

Some properties of K-frame in n-Hilbert space · Introduction · 0.97

What it cites

Cites as background 1 paper

[ref] Let ${ W_j }_ j ∈ J$ be a collection of closed subspaces of $H$ and ${ v_j }_ j ∈ J$ be a collection of positive weights and let $Λ_j ∈ ℬ ( H, H_j )$ for each $j ∈ J$.

Generalized fusion frames in Hilbert spaces · Preliminaries · 0.94

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