+91-674-249-4082

Submitted by klpatra on 19 February, 2018 - 17:17

Date/Time:

Monday, March 12, 2018 - 11:40 to 12:40

Venue:

SMS Seminar Hall

Speaker:

Deepika

Affiliation:

IIT Kanpur

Title:

Approximation Property and Its Variants in Weighted Spaces of Holomorphic Functions on Banach Spaces

Abstract:- Let $E$ be a complex Banach space and $U$ be an open subset of $E$.
Corresponding to a weight $w$(a strictly positive continuous
function) defined on U, the weighted space of holomorphic functions
is defined as $$\mathcal{H}_w(U) = \{ f\in \mathcal{H}(U) : \|f\|_w
= \sup_{x\in U}w(x)\|f(x)\|\leq 1\}.$$
The space $(\mathcal{H}_w(U),~ \|\cdot\|_w)$ is a dual Banach
space and its predual $\mathcal{G}_w(U)$ is given by
\begin{align*}
\mathcal{G}_w(U)=\{\phi \in \mathcal{H}_w(U)^\prime: \phi |B_w
~\textrm{is}~ \tau_0 -\textrm{continuous}\}
\end{align*}
where $B_w$ denotes the closed unit ball of the
weighted space $(\mathcal{H}_w(U),~ \|\cdot\|_w)$. In this talk,
we consider the approximation property and its variants for
$\mathcal{H}_w(U)$ and its predual $\mathcal{G}_w(U)$. After
introducing a locally convex topology $\tau_\mathcal{M}$ on these
spaces, we show that the weighted space equipped with the topology
$\tau_\mathcal{M}$ becomes topologically isomorphic to the class of
linear operators endowed with the topology of uniform convergence on
compact sets. This leads us to characterize the approximation
property for a complex Banach space $E$ in terms of the
approximation property for these spaces. Further, we characterize
the bounded approximation property for weighted Fr\'{e}chet and
(LB)-spaces using the techniques of $\mathcal{S}$-absolute
decompositions

**School of Mathematical Sciences**

NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

Corporate Site - This is a contributing Drupal Theme

Design by WeebPal.

Design by WeebPal.