Recently, parabolic equations in infinite dimensions have received much attention in literature (see, for example, Pa Prato [DP] and Da Prato Zabczyk [DZ]). In particular, Cannarsa and Da Prato [CD1] showed that the Laplacian (with a certain weight) generates a semigroup on BUC(H), the space of all bounded uniformly continuous functions on a separable Hilbert space H, which is called the heat s...

0 g(s, x(s), x(s− τ(s))) (t− s)1−α dω(s), t ∈ J = [0, T ], x(t) = ψ(t), t ∈ [−r, 0], (1.1) where 0 < α ≤ 1, T > 0 and A is a linear closed operator , defined on a given Hilbert space X . It is assumed that A generates an analytic semigroup S(t), t ≥ 0. The state x(.) takes its values in the Hilbert spaceX , and the control function u(.) is in L2(J, U), the Hilbert space of admissible control fu...

In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are  generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.

We give a characterization of all the unitarily invariant norms on finite von Neumann algebra acting separable Hilbert space. The is analogous to Neumann’s for $$n\times n$$ complex matrices and in Fang et al. (J Funct Anal 255(1):142–183, 2008) $$II_{1}$$ factors.

We present a generalisation of existing Lipschitz estimates for the stop and play operator for an arbitrary convex and closed characteristic, which contains the origin, in a separable Hilbert space. We are especially concerned with the dependence of stop and play on different scalar products.

This paper concerns the square-mean almost periodic solutions to a class of nonautonomous stochastic differential equations on a separable real Hilbert space. Using the so-called ‘Acquistapace-Terreni’ conditions, we establish the existence and uniqueness of a square-mean almost periodic mild solution to those nonautonomous stochastic differential equations.

In this paper we provide conditions under which a distribution is determined by just one randomly chosen projection. Then we apply our results to construct goodnessof-fit tests for the one and two-sample problems. We include some simulations as well as the application of our results to a real data set. Our results are valid for every separable Hilbert space.

The C*-algebra of bounded operators on the separable Hilbert space cannot be mapped to a W*-algebra in such a way that each unital commutative C*-subalgebra C(X) factors normally through `∞(X). Consequently, there is no faithful functor discretizing C*-algebras to W*-algebras this way.

As in the multivariate setting, the class of elliptical distributions on separable Hilbert spaces serves as an important vehicle and reference point for the development and evaluation of robust methods in functional data analysis. In this paper, we present a simple characterization of elliptical distributions on separable Hilbert spaces, namely we show that the class of elliptical distributions...

Let A be a separable unital C*-algebra and let π : A → L(H) be a faithful representation of A on a separable Hilbert space H such that π(A) ∩ K(H) = {0}. We show that OE , the Cuntz-Pimsner algebra associated to the Hilbert A-bimodule E = H⊗C A, is simple and purely infinite. If A is nuclear and belongs to the bootstrap class to which the UCT applies, then the same applies to OE . Hence by the ...