Smoothness and Weak* Sequential Compactness

Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces

We give a sequential compactness criterion for the weak topology of vector measures with values in certain nuclear spaces, such as the space S of all rapidly decreasing, infinitely differentiable functions, the space D of all test functions, and the strong duals of those spaces. This result contains Prokhorov–LeCam’s criterion for real measures and applies to cases which are not covered by März...

Weak Compactness of the Set of ε-Extensions

Bilateral composition operators on vector-valued Hardy spaces

Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$‎. ‎We investigate some operator theoretic properties of‎ ‎bilateral composition operator $C_{ph‎, ‎T}‎: ‎f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq‎ ‎+infty$.‎ ‎Compactness and weak compactness of $C_{ph‎, ‎T}$ on $H^p(X)$‎ ‎are characterized an...

Weak Convergence and Weak* Convergence1

In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In the first section, we proved some topological properties of dual spaces of real normed spaces. We used these theorems for proofs of Section 3. In Section 2, we defined weak convergence and weak* convergence, and proved some properties. By...

A uniform quantitative form of sequential weak compactness and Baillon’s nonlinear ergodic theorem

We apply proof-theoretic techniques of ‘proof mining’ to obtain an effective uniform rate of metastability in the sense of Tao for Baillon’s famous nonlinear ergodic theorem in Hilbert space. In fact, we analyze a proof due to Brézis and Browder of Baillon’s theorem relative to the use of weak sequential compactness. Using previous results due to the author we show the existence of a bar recurs...