On complete orthonormal sets in Hilbert space

Random sets of isomorphism of linear operators on Hilbert space

Abstract: This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator T on a Hilbert space with an orthogonal basis, we define the isomorphic structure Σ(T ) as the family of all subsets of the basis so that T restricted to their span is a nice isomorphism. Our main result is a dimension-free optimal estimate of the size of Σ(T ). It improve...

APPLICATIONS OF SOFT SETS IN HILBERT ALGEBRAS

The concept of soft sets, introduced by Molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. In this paper, weapply the notion of the soft sets of Molodtsov to the theory of Hilbert algebras.The notion of soft Hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...

Properties of Typical Bounded Closed Convex Sets in Hilbert Space

Baire category techniques are known to be a powerful tool in the investigation of the convex sets. Their use, which goes back to the fundamental contribution of Klee [17], has permitted to discover several interesting unexpected properties of convex sets (see Gruber [14], Schneider [23], Zamfirescu [25]). A survey of this area of research and additional bibliography can be found in [15, 27]. In...

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

Pointwise Bounds for Orthonormal Basis Elements in Hilbert Spaces