In this paper the controllability of a class impulsive neutral stochastic integro-differential systems driven by fractional Brownian motion and Poisson process in separable Hilbert space with infinite delay is studied. The result obtained using analysis fixed-point strategy. Finally, an illustrative example given to demonstrate effectiveness result.

We say that an uncountable metric space is computably categorical if every two computable structures on this space are equivalent up to a computable isometry. We show that Cantor space, the Urysohn space, and every separable Hilbert space are computably categorical, but the space C[0, 1] of continuous functions on the unit interval with the supremum metric is not. We also characterize computabl...

This paper is concerned with the controllability results of neutral impulsive stochastic functional integrodifferential equations driven by a fractional Brownian motion infinite delay in real separable Hilbert space. The are obtained using analysis, theory resolvent operator sense Grimmer and Krasnoselskii fixed point theorem. An example provided to illustrate theory.

A fundamental question in operator theory is: how rich is the collection of oprrators on a given Banach space? For classical spaces, especially Hilbert space, a well developed theory of operators exists. However a Banach space may have far fewer operators than one might expect. Shelah [S] has constructed a nonseparable Ba~lach space X , for which the space of operators with separable range has ...

In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the compact operators.) In this paper we establish that the analogous conclusion holds for a broad family of quotient algebras. Specifically, we will show that as...

In this paper, a new definition of numerical radius for adjointable operators in Hilbert -module space will be introduced. We also give a new proof of numerical radius inequalities for Hilbert space operators.

This paper is an investigation of the universal separable metric space up to isometry U discovered by Urysohn. A concrete construction of U as a metric subspace of the space C[0, 1] of functions from [0, 1] to the reals with the supremum metric is given. An answer is given to a question of Sierpiński on isometric embeddings of U in C[0, 1]. It is shown that the closed linear span of an isometri...

We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was introduced by Székely, Rizzo and Bakirov, to general metric spaces. We show that for testing independence, it is necessary and sufficient that the metric space be of strong negative type. In particular, we show that this holds for separable Hilbert spaces, which answers a question of Kosorok. Instead of t...