Dedicated to the memory of Al Cliiord, a wonderful mathematician and a wonderful man. Abstract Of concern are semigroups of linear norm one operators on Hilbert space of the form (discrete case) T = fT n : n = 0; 1; 2; g or (continuous case) T = fT (t) : t 0g: Using ergodic theory and Hilbert-Schmidt operators, the Cess aro limits (as n! 1) of j< T n f; f >j 2 ; j< T (n)f; f >j 2 are computed (...

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

This paper is concerned with a technique for solving Fredholm integro-dierentialequations in the reproducing kernel Hilbert space. In contrast with the conventionalreproducing kernel method, the Gram-Schmidt process is omitted hereand satisfactory results are obtained. The analytical solution is represented inthe form of series. An iterative method is given to obtain the approximate solution.Th...

In this paper some new positive results in the Operator Corona Problem are obtained in rather general situation. The main result is that under some additional assumptions about a bounded analytic operator-valued function F in the unit disc D the condition F (z)F (z) ≥ δI ∀z ∈ D (δ > 0) implies that F has a bounded analytic left inverse. Typical additional assumptions are (any of the following):...

&lt;p style='text-indent:20px;'&gt;In the following work, we consider Boltzmann equation that models a diatomic gas by representing microscopic internal energy continuous variable I. Under some convenient assumptions on collision cross-section &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ \mathcal{B} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, prove linearized ope...

In this paper, by using the way of weight coecients and technique of real analysis, a multidimensionaldiscrete Hilbert-type inequality with a best possible constant factor is given. The equivalentform, the operator expression with the norm are considered.

In these lectures we shall present an introduction of the theory of stochastic integration in UMD Banach spaces and some of its applications. The Hilbert space approach to stochastic partial differential equations (SPDEs) was pioneered in the 1980s by Da Prato and Zabczyk. Under suitable Lipschitz conditions, mild solutions of semilinear SPDEs in Hilbert spaces can be obtained by solving a fixe...

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...

for a bounded linear operator on hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎we study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎also we show that any quasinilpotent operator $t$ has an hypernoncyclic vector‎, ‎and so $t$ has a nontrivial hyperinvariant subspace‎.