The inequality between rank and crank moments was conjectured and later proved by Garvan himself in 2011. Recently, Dixit and the authors introduced finite ana- logues of rank and crank moments for vector partitions while ...

Ramanujan recorded five interesting q-series identities in a section that is not as systematically arranged as the other chapters of his second notebook. These five identities do not seem to have acquired enough attention. ...

In this paper, we discuss the decomposability of weighted composition operator $uC_\phi$ on $L^p(X)(1\leq p<\infty)$ of a $\sigma$-finite atomic measure space $(X,\mathcal{S},\mu)$ with the assumption that $u\in L^\infty(X)$ ...

We extend and study the notion of bounded point evaluation introduced by Williams for a cyclic operator to the class of operators with the wandering subspace property. We characterize the set bpe(T) of all bounded point ...

In this paper, we discuss the decomposability and single valued extension property of composition operators Cφ on Lp(X)(1 ≤ p < ∞) spaces. We give a sufficient condition for non-decomposability of Cφ in terms of ...

Given a directed Cartesian product T of locally finite, leafless, rooted directed trees T1,…,Td of finite joint branching index, one may associate with T the Drury-Arveson-type C[z1,…,zd]-Hilbert module Hca(T) of vector-valued ...

In this paper, we give a condition under which a bounded linear operator on a complex Banach space has Single Valued Extension Property (SVEP) but does not have decomposition property (±). We also discuss the analytic ...

The wandering subspace problem for an analytic norm-increasing -isometry on a Hilbert space asks whether every -invariant subspace of can be generated by a wandering subspace. An affirmative solution to this problem for ...

We systematically develop the multivariable counterpart of the theory of weighted shifts on rooted directed trees. Capitalizing on the theory of product of directed graphs, we introduce and study the notion of multishifts ...

Let R be a commutative ring with unity and S be a (unital) subring of R such that R is integral over S and S⊆R has FCP. Let M be an R-module. For any submodule N of M, it is shown that R(+)N⊆R(+)M has FCP if and only if ...