Let H be an innite dimensional Hilbert space and K(H) be the set of all compactoperators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate ofhigher derivation and higher Jordan derivation on K(H) associated with the following Cauchy-Jensentype functional equation 2f((T + S)/2+ R) = f(T ) + f(S) + 2f(R) for all T, S, R are in K(...

Let X be a geodesic space. We say that X is geodesically complete if every geodesic segment β : [0, a] → X from β(0) to β(a) can be extended to a geodesic ray α : [0,∞) → X, (i.e. β(t) = α(t), for 0 ≤ t ≤ a). If X is a compact npc space (“npc” means: “non-positively curved”) then it is almost geodesically complete, see [10]. (X, with metric d, is almost geodesically complete if its universal co...

The Gibbs random field (GRF) has proved to be a simple and practical way of parameterizing the Markov random field, which has been widely used to model an image or image-related process in many image processing applications. In particular, the GRF can be employed to construct an efficient Bayesian estimation that often yields optimal results. We describe how the GRF can be efficiently incorpora...

for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Let G be a locally compact group, and let WAP(G) denote the space of weakly almost periodic functions on G. We show that, if G is a [SIN]-group, but not compact, then the dual Banach algebra WAP(G)∗ does not have a normal, virtual diagonal. Consequently, whenever G is an amenable, non-compact [SIN]-group, WAP(G)∗ is an example of a Connes-amenable, dual Banach algebra without a normal, virtual ...

Let G be a locally compact group, and let WAP(G) denote the space of weakly almost periodic functions on G. We show that, if G is a [SIN]-group, but not compact, then the dual Banach algebra WAP(G)∗ does not have a normal, virtual diagonal. Consequently, whenever G is an amenable, non-compact [SIN]-group, WAP(G)∗ is an example of a Connes-amenable, dual Banach algebra without a normal, virtual ...

Let G be a locally compact group, and let WAP(G) denote the space of weakly almost periodic functions on G. We show that, if G is a [SIN]-group, but not compact, then the dual Banach algebra WAP(G)∗ does not have a normal, virtual diagonal. Consequently, whenever G is an amenable, non-compact [SIN]-group, WAP(G)∗ is an example of a Connes-amenable, dual Banach algebra without a normal, virtual ...