Pointwise Boundedness and Equicontinuity in Β-duals

نویسندگان

  • CHARLES SWARTZ
  • Charles Swartz
چکیده

Let E be a vector valued sequence space with operator valued βdual E . If E satisfies certain gliding hump assumptions, we show that pointwise bounded subsets of E are sequentially equicontinuous. The result is established by considering uniform convergence of the elements in E .

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Weak Convergence and Fluid Limits in Optimal Time-to-Empty Queueing Control Problems

We consider a simple class of controlled queue length processes in the fluid rescaling, X(t) = 1 n X(nt). Consider the optimal control problem for X(t) which consists of minimizing the integral of an undiscounted positive running cost until the first time that X = 0. Our main result uses weak convergence ideas to show that the optimal value functions V n of the stochastic control problems for X...

متن کامل

On Principle of Equicontinuity

The main purpose of this paper is to prove some results of uniform boundedness principle type without the use of Baire’s category theorem in certain topological vector spaces; this provides an alternate route and important technique to establish certain basic results of functional analysis. As applications, among other results, versions of the Banach-Steinhaus theorem and the Nikodym boundednes...

متن کامل

Singularities and equicontinuity of certain families of set-valued mappings

In the present paper we establish an abstract principle of condensation of singularities for families consisting of set-valued mappings. By using it as a basic tool, the condensation of the singularities and the equicontinuity of certain families of generalized convex set-valued mappings are studied. In particular, a principle of condensation of the singularities of families of closed convex pr...

متن کامل

An Ascoli Theorem for Sequential Spaces

Ascoli theorems characterize “precompact” subsets of the set of morphisms between two objects of a category in terms of “equicontinuity” and “pointwise precompactness,” with appropriate definitions of precompactness and equicontinuity in the studied category. An Ascoli theorem is presented for sets of continuous functions from a sequential space to a uniform space. In our development we make ex...

متن کامل

ON COMPACT OPERATORS ON SOME SPACES RELATED TO MATRIX B ( r , s )

Many sequence spaces arise from different concepts of summability. Recent results obtained by Altay, Başar and Malkowsky [2] are related to strong Cesàro summability and boundedness. They determined β−duals of the new sequence spaces and characterized some classes of matrix transformations on them. Here, we will present new results supplementing their research with the characterization of class...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010