Related papers: $K_{0}$-groups and strongly irreducible decomposit…

We construct a large family of positive-definite kernels $K: \mathbb{D}^n\times \mathbb{D}^n \to \mbox{M} (r, \mathbb C)$, holomorphic in the first variable and anti-holomorphic in the second, that are quasi-invariant with respect to the…

Strongly irreducible operators can be considered as building blocks for bounded linear operators on complex separable Hilbert spaces. Many bounded linear operators can be written as direct sums of at most countably many strongly irreducible…

Let $\mathcal{M}$ be a separable von Neumann algebra with center $\mathcal{Z}(\mathcal{M})$. An operator $T$ in $\mathcal{M}$ is called irreducible if the von Neumann algebra $W^*(T)$ generated by $T$ has trivial relative commutant, i.e.,…

The homotopy groups of the (stabilized) group of invertible pseudodifferential operators of order zero acting on a closed manifold X are computed in terms of the K-theory of the cosphere bundle S*X. At the same time, we show that the…

An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is said to be isometric if the operator $[V_1\...\ V_n]:H^n\to H$ is an isometry. We prove a decomposition for an isometric tuple of operators that generalizes the…

Let $\mathcal M$ be a factor von Neumann algebra with separable predual and let $T\in \mathcal M$. We call $T$ an irreducible operator (relative to $\mathcal M$) if $W^*(T)$ is an irreducible subfactor of $\mathcal M$, i.e., $W^*(T)'\cap…

Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that…

A commuting tuple of operators $(S_1,\dots, S_{n-1},P)$, defined on a Hilbert space $\mathcal H$, for which the closed symmetrized polydisc \[ \Gamma_n =\left\{ \left(\sum_{1\leq i\leq n} z_i,\sum_{1\leq i<j\leq n}z_iz_j,\dots,…

Let $\Omega$ be an irreducible bounded symmetric domain of rank $r$ in $\mathbb C^d.$ Let $\mathbb K$ be the maximal compact subgroup of the identity component $G$ of the biholomorphic automorphism group of the domain $\Omega$. The group…

The classical Cowen-Douglas class of (commuting tuples of) operators possessing an open set of (joint) eigenvalues of finite constant multiplicity was introduced by Cowen and Douglas, generalizing the backward shifts. Their unitary…

Let $\mathcal U(d)$ be the group of $d\times d$ unitary matrices. We find conditions to ensure that a $\mathcal U(d)$-homogeneous $d$-tuple $\boldsymbol T$ is unitarily equivalent to multiplication by the coordinate functions on some…

In this paper, we will show that for an operator $T$ which is injective and has dense range, there exists an invertible operator $X$ (in fact we can find $U+K$, where $U$ is an unitary operator and $K$ is a compact operator with norm less…

Let $T$ be a bounded quaternionic normal operator on a right quaternionic Hilbert space $\mathcal{H}$. We show that $T$ can be factorized in a strongly irreducible sense, that is, for any $\delta >0$ there exist a compact operator $K$ with…

The curvature $\mathcal K_T(w)$ of a contraction $T$ in the Cowen-Douglas class $B_1(\mathbb D)$ is bounded above by the curvature $\mathcal K_{S^*}(w)$ of the backward shift operator. However, in general, an operator satisfying the…

Let $\mathcal M$ be a separable factor. An operator $T$ in $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann algebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e.,…

An operator $T$ in a separable factor $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann subalgebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e., $W^*(T)'\cap\mathcal{M}=\mathbb{C}I$.…

This paper aims to study reducible and irreducible approximation in the set $\textsl{CSO}$ of all complex symmetric operators on a separable, complex Hilbert space $\mathcal H$. When ${\rm dim} \mathcal H=\infty$, it is proved that both…

An \textit{ideal} of $N$-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with…

The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentions of compact quantum group algebras are deduced first in both the right and left regular coaction formalisms. In each case it…

A theorem of N. Katz \cite{Ka} p.45, states that an irreducible differential operator $L$ over a suitable differential field $k$, which has an isotypical decomposition over the algebraic closure of $k$, is a tensor product $L=M\otimes_k N$…