arXiv subjects

Deepika Baweja

Publications and source records attributed to Deepika Baweja.

3 recordsLinked to original sources

arXiv2024

A generalised mid summability in Banach spaces

In this paper, we study the notion of mid summability in a general setting using the duality theory of sequence spaces. We define the vector valued sequence space $λ^{mid}(X)$ corresponding to a Banach space $X$ and sequence space $λ$. We prove that $λ^{mid}(\cdot)$ can be placed in a chain with the vector valued sequence spaces $λ^{s}(\cdot)$ and $λ^{w}(\cdot)$. Consequently, we define mid $λ$-summing operators and obtain the maximality of these operator ideals for a suitably restricted $λ$. Furthermore, we define a tensor norm using the vector valued sequence spaces $λ^{s}(\cdot)$ and $λ^{mid}(\cdot)$, and establish its correspondence with the operator ideal of absolutely mid $λ$-summing operators.

math.FA↗

arXiv2021

Characterizations of approximation properties defined by operator ideals in the predual of weighted Banach spaces of holomorphic functions

In this article, we show that the predual $\mathcal{G}_w(U)$ of the weighted space of holomorphic functions has the $\mathcal{I}$- approximation property if and only if $E$ has the $\mathcal{I}$- approximation property, where $\mathcal{I}$ is a suitably chosen operator ideal, and $\it{w}$ is a radial weight defined on a balanced open subset U of a Banach space $E$.

math.FA↗

arXiv2021

Ideals of mid p-summing operators: a tensor product approach

In this article, we study the ideals of mid $p$-summing operators. We obtain representation of these operator ideals by tensor norms. These tensor norms are defined by using a particular kind of sequential dual of the class of mid $p$-summable sequences. As a consequence, we prove a characterization of the adjoints of weakly and absolutely mid $p$-summing operators in terms of the operators that are defined by the transformation of dual spaces of certain vector-valued sequence spaces.

math.FA↗