Related papers: Invariant Subspace Problem in Hilbert Spaces: Expl…
We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space…
This is a series of 5 lectures around the common subject of the construction of self-adjoint extensions of symmetric operators and its applications to Quantum Physics. We will try to offer a brief account of some recent ideas in the theory…
In this paper we present a systematic study of regular sequences of quasi-nonexpansive operators in Hilbert space. We are interested, in particular, in weakly, boundedly and linearly regular sequences of operators. We show that the type of…
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
In this work we study the following three space problem for operator spaces: if X is an operator space with base space isomorphic to a Hilbert space and X contains a completely isomorphic copy of the operator Hilbert space OH with…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry…
We present some old and new results on a class of invariant spaces of holomorphic functions on symmetric domains, both in their circular bounded realizations and in their unbounded realizations as Siegel domains of type II. These spaces…
The multiple-quantum NMR spectroscopy has an extensive application in determination of the bio-macro-molecular structures and in the investigation of the properties of a variety of physical materials. In quantum computation the…
We prove that if T is an operator on an infinite-dimensional Hilbert space whose spectrum and essential spectrum are both connected and whose Fredholm index is only 0 or 1, then the only nontrivial norm-stable invariant subspaces of T are…
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
In modeling quantum systems or wave phenomena, one is often interested in identifying eigenstates that approximately carry a specified property; scattering states approximately align with incoming and outgoing traveling waves, for instance,…
We revisit the work of Rieffel and van Daele on pairs of subspaces of a real Hilbert space, while relaxing as much as possible the assumption that all the relevant subspaces are in general positions with respect to each other. We work out,…
In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator…
In this paper we completely characterize the norm attainment set of a bounded linear operator on a Hilbert space. This partially answers a question raised recently in [\textit{D. Sain, On the norm attainment set of a bounded linear…
Let $T$ be an absolutely continuous polynomially bounded operator, and let $\theta$ be a singular inner function. It is shown that if $\theta(T)$ is invertible and some additional conditions are fulfilled, then $T$ has nontrivial…
This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex…
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.…