Related papers: Powers of posinormal operators
A bounded linear operator $A$ on a Hilbert space $\mathcal{H}$ is posinormal if there exists a positive operator $P$ such that $AA^{*} = A^{*}PA$. We show that if $A$ is posinormal with closed range, then $A^n$ is posinormal and has closed…
A bounded linear operator $A$ on a Hilbert space is posinormal if there exists a positive operator $P$ such that $AA^{*} = A^{*}PA$. Posinormality of $A$ is equivalent to the inclusion of the range of $A$ in the range of its adjoint $A^*$.…
In the recent paper, R. E. Curto, S. H. Lee, J. Yoon, asked the following question: Let $A$ be a subnormal operator, and assume that $A^2$ is quasinormal. Does it follow that $A$ is quasinormal? In this paper, we give an affirmative answer…
The paper extends three results regarding the nth root problem by embedding classes of Hilbert-space operators into the class of posinormal operators. For instance, it is shown that (i) for coposinormal operators, if T is paranormal and T^n…
In [9] a question is raised: if a power bounded operator is quasisimilar to a singular unitary operator, is it similar to this unitary operator? For polynomially bounded operators, a positive answer to this question is known [1], [13]. In…
The starting place is a brief proof of a well-known result, the hyponormality of $C_k$ (the generalized Ces\`{a}ro operator of order one) for $k \geq 1$. This leads to the definition of a superclass of the posinormal operators. It is shown…
In a recent paper [9], R. E. Curto, S. H. Lee and J. Yoon asked the following question: Let $T$ be a subnormal operator, and assume that $T^2$ is quasinormal. Does it follow that $T$ is quasinormal?. In [36] we answered this question in the…
We focus on two problems relating to the question of when the product of two posinormal operators is posinormal, giving (1) necessary conditions and sufficient conditions for posinormal operators to have closed range, and (2) sufficient…
This paper introduces and investigates the class of \textit{$k$-quasi $n$-power posinormal operators} in Hilbert spaces, generalizing both posinormal and $n$-power posinormal operators. We establish fundamental properties including matrix…
If $T$ is a polynomially bounded operator, $\mathcal M$ is an invariant subspace of $T$, $T|_{\mathcal M}$ is a unilateral shift and $T^*|_{\mathcal M^\perp}$ is subnormal, then $T$ has a nontrivial hyperinvariant subspace. If an operator…
We study jointly quasinormal and spherically quasinormal pairs of commuting operators on Hilbert space, as well as their powers. We first prove that, up to a constant multiple, the only jointly quasinormal $2$-variable weighted shift is the…
Families of quasi-permutable normal operators in octonion Hilbert spaces are investigated. Their spectra are studied. Multiparameter semigroups of such operators are considered. A non-associative analog of Stone's theorem is proved.
In this paper, some sub-classes of paranormal weighted conditional expectation type operators, such as *-paranormal, quasi-*-paranormal and (n; k)-quasi-*-paranormal weighted conditional expectation type opera- tors on $L^2(\Sigma)$ are…
In this paper, we study quasinormal and hyponormal composition operators \W with linear fractional compositional symbol $\ph$ on the Hardy and weighted Bergman spaces. We characterize the quasinormal composition operators induced on $H^{2}$…
A quasi-product on the normed space is defined. In addition, the notions of the eigenvectors of a linear operator can be extended for the nonlinear operator. Based on the quasi-product and the generalized eigenvectors, the spectral theorems…
Partial operators can have void or unbounded spectra. Contrarily to what is written in Dunford-Schwarz, the reason is not in the fact they are unounded operators.
For nonnegative integers $n$ and $k$, we introduce in this paper a new class of $(n,k)$-quasi-*-paranormal operators satisfying $$||T^{1+n}(T^{k}x)||^{1/(1+n)}||T^{k}x||^{n/(1+n)} \geq ||T^*(T^{k}x)|| \makebox{\ for all} x \in H.$$ This…
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…
In this article, the posinormality and coposinormality of weighted composition-differentiation operators on Hardy space $H^2(\mathbb{D})$ are investigated. It is observed that while a composition-differentiation operator $D_{\phi,n}$ fails…
In this paper we attempt to lay the foundations for a theory encompassing some natural extensions of the class of subnormal operators, namely the $n$--subnormal operators and the sub-$n$--normal operators. We discuss inclusion relations…