Related papers: Normals, subnormals and an open question
A criterion for subnormality of unbounded composition operators in L2-spaces, written in terms of measurable families of probability measures satisfying the so-called consistency condition, is established. It becomes a new characterization…
Here I briefly discuss why supersymmetry is considered a leading candidate of physics beyond the standard model. I also highlight the salient features of different supersymmetry breaking models. A few other symmetries, broken or intact,…
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…
Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $\CAlg{A}$. New classes of (possibly unbounded) operators $t:E\to F$ are introduced and investigated. Instead of the density of the domain $\Def(t)$ we only assume that $t$ is…
Consideration of certain properties of group rings and their ideals search
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators.…
Resource allocation problems are a fundamental domain in which to evaluate the fairness properties of algorithms. The trade-offs between fairness and utilization have a long history in this domain. A recent line of work has considered…
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…
In the work the fair division problem for two participants in presence of both divisible and indivisible items is considered. The set of all divisions is formally described; it is demonstrated that fair (in terms of Brams and Taylor)…
We pursue the study of families of functions on the natural numbers, with emphasis here on the bounded families. The situation being more complicated than the unbounded case, we attack the problem by classifying the families according to…
In this paper, the notion of pronormal L-subgroups of an L-group has been introduced by using the concept of conjugate L-subgroup. The notion of pronormal L-subgroups has been investigated in context of normality and subnormality of…
Let $T\in\mathbb{B}(\mathscr{H})$ and $T=U|T|$ be its polar decomposition. We proved that (i) if $T$ is log-hyponormal or $p$-hyponormal and $U^n=U^\ast$ for some $n$, then $T$ is normal; (ii) if the spectrum of $U$ is contained in some…
In this paper we provide a new set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are "fine-grained" compared with the…
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…
Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
An operational description of quantum phenomena concerns developing models that describe experimentally observed behaviour. $\textit{Higher-order quantum operations}\unicode{x2014}$quantum operations that transform quantum…
The paper is devoted to the investigation of uniform notion for acts over semigroups perceived as an overclass of subdirectly irreducible acts. We establish conditions to fill the gap between these classes of acts. Besides we prove that…
Bounded and unbounded weighted composition operators on $L^2$ spaces over $\sigma$-finite measure spaces are investigated. A variety of questions related to seminormality of such operators are discussed.
We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of…