In this paper, we consider a class of generalized closed linear manifolds in a nonseparable Hilbert spaceH, which is closely related to the generalized Fredholm theory. We first investigate properties of the setB={T鈭圡:T(H)A(H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\use...
In this paper, we define some new topologies related to a nonseparable Hilbert space H, which are generalizations of the well-known strong operator topology (SOT), weak operator topology (WOT) on B(H) and the weak topology on H. We study properties of these new topologies, and obtain some...
Given a bipartite quantum system represented by a tensor product of two Hilbert spaces, we give an elementary argument showing that if either component space is infinite-dimensional, then the set of nonseparable density operators is trace-norm dense in the set of all density operators (and the ...
nonseparable Banach spaceuncountable unconditional basisK_x0002_BesseliannessK-HilbertiannessWe consider the uncountable K-Besselness and K-Hilbertness of systems in nonseparable Banach spaces with respect to nonseparable Banach space of systems of scalars K. The criteria for K-Besselness and K-...
We use the remarkable distance estimate of Ilya Kachkovskiy and Yuri Safarov, to show that if $H$ is a nonseparable Hilbert space and $K$ is any closed ideal in $B(H)$ that is not the ideal of compact operators, then any normal element of $B(H)/K$ can be lifted to a normal...
Here, E E mathContainer Loading Mathjax denotes the famed Erds space introduced by Paul Erds as 'rational points in Hilbert space', the subspace of Hilbert space consisting of vectors of which all coordinates are rational.doi:10.1016/j.topol.2011.05.045Jan J. Dijkstra...
The former relates to the time it takes an acoustic wave to travel at its velocity along some path in the space it propagates. However, the geometric phase depends on the degrees of freedom of this wave that form its Hilbert space. The state of this wave is a vector in the Hilbert ...