On the definition of fuzzy Hilbert spaces and its application.
On the existence of configurations of subspaces in a Hilbert space with fixed angles.
On the radius of a set in a Hilbert space
On three problems from the Scottish Book connected with orthogonal systems
On Typical Compact Convex Sets in Hilbert Spaces
Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.
On Wigner's theorem: Remarks, complements, comments, and corollaries.
Order properties of splitting subspaces in an inner product space
Orthogonality in normed linear spaces: a classification of the different concepts and some open problems.
Orthogonality in inner products is a binary relation that can be expressed in many ways without explicit mention to the inner product of the space. Great part of such definitions have also sense in normed linear spaces. This simple observation is at the base of many concepts of orthogonality in these more general structures. Various authors introduced such concepts over the last fifty years, although the origins of some of the most interesting results that can be obtained for these generalized concepts...
Ortogonalita na množinách