Related papers: A distance between operators acting in different H…
We consider pairs of quantum observables (POVMs) and analyze the relation between the notions of non-disturbance, joint measurability and commutativity. We specify conditions under which these properties coincide or differ---depending for…
In this paper, we give the complete description of maps on self-adjoint bounded operators on Hilbert space which preserve a triadic relation involving the difference of operators and either commutativity or quasi-commutativity in both…
We show that the norm of the commutator defines "almost a metric" on the quotient space of commuting matrices, in the sense that it is a semi-metric satisfying the triangle inequality asymptotically for large matrices drawn from a "good"…
We initiate the study of the small scale geometry of operator spaces. The authors have previously shown that a map between operator spaces which is completely coarse (that is, the sequence of its amplifications is equi-coarse) must be…
This article introduces several new relations among related Hilbert space operators. In particular, we prove some L\"{o}ewner partial orderings among $T, |T|, \mathcal{R}T, \mathcal{I}T, |T|+|T^*|$ and many other related forms, as a new…
We study Rellich inequalities associated to higher-order elliptic operators in the Euclidean space. The inequalities are expressed in terms of an associated Finsler metric. In the case of half-spaces we obtain the sharp constant while for a…
The paper is concerned with the following question: if $A$ and $B$ are two bounded operators between Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$, and $\mathcal{M}$ and $\mathcal{N}$ are two closed subspaces in $\mathcal{H}$, when will…
Covering ill-posed problems with compact and non-compact operators regarding the degree of ill-posedness is a never ending story written by many authors in the inverse problems literature. This paper tries to add a new narrative and some…
The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal…
New inequalities for the $A$-numerical radius of the products and sums of operators acting on a semi-Hilbert space, i.e. a space generated by a positive semidefinite operator $A$, are established. In particular, it is proved for operators…
Let $(X, d)$ be a compact metric space and let $\mathcal{M}(X)$ denote the space of all finite signed Borel measures on $X$. Define $I \colon \mathcal{M}(X) \to \R$ by \[I(\mu) = \int_X \int_X d(x,y) d\mu(x) d\mu(y),\] and set $M(X) = \sup…
We develop a duality theory for unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency…
We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…
Observables in quantum mechanics are represented by self-adjoint operators on Hilbert space. Such ubiquitous, well-known, and very foundational fact, however, is traditionally subtle to be explained in typical first classes in quantum…
S-metric and b-metric spaces are metrizable, but it is still quite impossible to get an explicit form of the concerned metric function. To overcome this, the notion of $\phi$-metric is developed by making a suitable modification in triangle…
This paper defines and establishes relations among approximation spaces of certain operators called \textit{H-operators}, which generalize the notion of self-adjoint to Banach spaces.
Denote by w(A) the numerical radius of a bounded linear operator A acting on Hilbert space. Suppose that A is invertible and that the numerical radius of A and of its inverse are no greater than 1+e for some non-negative e. It is shown that…
This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…