Common fixed points for maps on cone metric space

The purpose of this paper is to generalize and to unify fixed point theorems of Das and Naik, ?iri?, Jungck, Huang and Zhang on complete cone metric space.     

Category with a natural cone

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is to give full details of the foregoing.     

A Hilbert $$C^*$$ -Module with Extremal Properties

Functional Analysis and Its Applications - We construct an example of a Hilbert $$C^*$$ -module which shows that Troitsky’s theorem on the geometric essence of $$ {\mathcal A} $$ -compact...     

Linear maps preserving the minimum and surjectivity moduli of Hilbert space operators

Let B(H) be the algebra of all bounded linear operators on a complex infinite-dimensional Hilbert space H. For every T∈B(H), let m(T) and q(T) denote the minimum modulus and surjectivity modulus of T respectively. Let ?:B(H)→B(H) be a surjective linear map. In this paper, we prove that the following assertions are equivalent:

(i)

m(T)=m(?(T)) for all T∈B(H),

(ii)

q(T)=q(?(T)) for all T∈B(H),

(iii)

there exist two unitary operators U,V∈B(H) such that ?(T)=UTV for all T∈B(H).

This generalizes the result of Mbekhta [7, Theorem 3.1] to the non-unital case.     

Quantum symmetry groups of Hilbert modules equipped with orthogonal filtrations

We define and show the existence of the quantum symmetry group of a Hilbert module equipped with an orthogonal filtration. Our construction unifies the constructions of Banica–Skalski?s quantum symmetry group of a C^?$C^{?}$-algebra equipped with an orthogonal filtration and Goswami?s quantum isometry group of an admissible spectral triple.     

Sampling in a Hilbert space

An analog of the Whittaker-Shannon-Kotel'nikov sampling theorem is derived for functions with values in a separable Hilbert space. The proof uses the concept of frames and frame operators in a Hilbert space. One of the consequences of this theorem is that it allows us to derive sampling theorems associated with boundary-value problems and some homogeneous integral equations, which in turn gives us a generalization of another sampling theorem by Kramer.

     

Diffusion with irregular drift in a Hilbert space

We construct a generalized diffusion process in a separable Hilbert space. The drift of this process satisfies certain conditions of integrability with respect to the Gaussian measure. We establish the properties of the constructed process.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 9, pp. 1224–1230, September, 1995.     

Locating subsets of a Hilbert space

This paper deals with locatedness of convex subsets in inner product and Hilbert spaces which plays a crucial role in the constructive validity of many important theorems of analysis.

     

Completely p-summing maps on the operator Hilbert space OH

We prove the completely p-summing ideals of OH are all equal as sets for 1?p<2. A phase transition then occurs at p=2 as we also show for p?2, the completely p-summing ideals of OH turn out as sets to be Schatten ideal classes with the limiting case being the Schatten 4-class ideal S₄ when p→∞.     

Hilbert cube manifolds of maps

The purpose of this note is to illustrate in the simplest possible terms how a function space may be a Hilbert Cube (= Q) manifold. It is shown that certain spaces of “rectifiable” maps from a compact Riemannian manifold to a flat Kiemannian manifold are Q-manifolds. For example: if α > 0, the space of loops of length ⩽α in a flat manifold is a Q-manifold. No prior knowledge of Riemannian geometry is required.     

Limit-ill-posed equations in a Hilbert space

The behavior of the solution of a limit-ill-posed problem on fixed compacta is investigated for integral operators, acting in a Hilbert space.Translated from Ukrainskii Matematicheskii Zhurnal, vol. 43, No. 2, pp. 241–247, February, 1991.