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 ...
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 ...
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 ...
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 ...
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 ...
Recently, Hartz proved that every commuting contractive classical multishift with non-zero weights satisfies the matrix-version of von Neumann’s inequality. We show that this result does not extend to the class of commuting ...
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 ...
Motivated by the theory of weighted shifts on directed trees and its multivariable counterpart, we address the question of identifying commutant and reflexivity of the multiplication d-tuple on a reproducing kernel Hilbert ...
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 ...
Let T = (V, E) be a leafless, locally finite rooted directed tree.
We associate with T a one parameter family of Dirichlet spaces Hq (q
1), which turn out to be Hilbert spaces of vector-valued holomorphic
functions ...
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 be a rooted directed tree with finite branching index
, and let
be a left-invertible weighted shift on . We show that
can be modelled as a multiplication operator
on a reproducing kernel Hilbert space of -valued ...
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 ...
The following result was proved in [5,Remark 2.2].
Theorem 0.1. If R T are Noetherian rings such that there does not
exist any integrally dependent adjacent Noetherian rings between them, then
for each ¯c/¯b 2 T/Z ...
Let R be a commutative ring with identity. The ring R × R can be
viewed as an extension of R via the diagonal map : R →֒ R×R, given
by (r) = (r, r) for all r ∈ R. It is shown that, for any a, b ∈ R, the
extension ...
The notion of maximal non valuative domain is introduced and characterized.
An integral domain R is called a maximal non valuative domain
if R is not a valuative domain but every proper overring of R is
a valuative ...
Let R be a commutative ring with unity. The notion of maximal non valuation
domain in an integral domain is introduced and characterized. A proper subring R of an
integral domain S is called a maximal non valuation domain ...
Let R be a commutative ring with identity. If a ring R is contained in an arbitrary union of rings, then R is contained in one of them under various conditions. Similarly, if an arbitrary intersection of rings is contained ...