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 generalize the notion of bounded point evaluation introduced by Williams for a cyclic operator to a finitely multicyclic commuting d-tuple of bounded linear operators on a complex separable Hilbert space. We show that ...

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 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 construct an analytic norm-increasing 3-isometric weighted shift on a rootless directed tree, which does not have the wandering subspace property. This answers a question of Shimorin [S2001, p. 185] in the negative. The ...

LetApDqdenote the disk algebra. Every endomorphism ofApDqis inducedby someφPApDqwith}φ}≤1. In this paper, it is shown that ifφis not an automorphismofDandφhas a fixed point in the open unit disk then the endomorphism induced ...

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 ...