arXiv subjects

Hemalatha M

Publications and source records attributed to Hemalatha M.

3 recordsLinked to original sources

arXiv2026

Frame related sequences in tensor product of Hilbert spaces

We study frames and related sequences in tensor products of separable Hilbert spaces from an algebraic perspective. For sequences $\{f_n\}_{n\in\mathbb{N}} \subset H_1$ and $\{g_m\}_{m\in\mathbb{N}} \subset H_2$, we consider the tensor sequence $\{f_n \otimes g_m\}_{n,m\in\mathbb{N}}$ in $H_1 \otimes H_2$. We characterize the lower semi-frame and Riesz--Fischer properties of tensor sequences in terms of the corresponding properties of the component sequences. These results extend to infinite tensor products. In addition, we study the action of tensor sums of operators on frame-related sequences in tensor product Hilbert spaces.

math.FA↗

arXiv2026

Characterization of Frame-Related Sequences on Semi-Hilbert Spaces

Let $A\in\mathcal{B}(H)^+$ and $B\in\mathcal{B}(\ell^2)^+$ be positive bounded operators. We investigate reduced weighted adjoints of densely defined closable operators and use them to develop frame-type systems in the semi-Hilbert spaces induced by $A$ and $B$. Closedness, boundedness, range behavior, and algebraic properties of the $A$-adjoint are established, with particular attention to sums, products, and double adjoints in the unbounded setting. We then study the associated $AB$-analysis, $AB$-synthesis, and $AB$-frame operators. Operator-theoretic characterizations of $AB$-Bessel sequences, $AB$-lower semi-frames, and $AB$-frames are obtained, and examples show that several natural weighted-adjoint identities may hold only as proper inclusions. A Douglas-type range characterization for $AB$-frames is also derived.

math.FA↗

arXiv2025

Direct Sum of Lower Semi-Frames in Hilbert Spaces

In this paper, structural properties of lower semi-frames in separable Hilbert spaces are explored with a focus on transformations under linear operators (may be unbounded). Also, the direct sum of lower semi-frames, providing necessary and sufficient conditions for the preservation of lower semi-frame structure, is examined.

math.FA↗