A Weierstrass theorem for real Banach spaces

A Stone-weierstrass Type Theorem for Semiuniform Convergence Spaces

A Stone-Weierstraß type theorem for semiuniform convergence spaces is proved. It implies the classical Stone-Weierstraß theorem as well as a Stone-Weierstraß type theorem for filter spaces due to Bentley, Hušek and Lowen-Colebunders [1].

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Kreps-yan Theorem for Banach Ideal Spaces

Let C be a closed convex cone in a Banach ideal space X on a measurable space with a σ-finite measure. We prove that conditions C ∩ X+ = {0} and C ⊃ −X+ imply the existence of a strictly positive continuous functional on X , whose restriction to C is non-positive. Let (Ω,F ) be a measurable space, which is complete with respect to a measure (that is, a countably-additive function) μ : F 7→ [0,∞...

A Quasi-invariance Theorem for Measures on Banach Spaces

We show that for a measure -y on a Banach space directional different ¡ability implies quasi-translation invariance. This result is shown to imply the Cameron-Martin theorem. A second application is given in which 7 is the image of a Gaussian measure under a suitably regular map.

A quantitative Mean Ergodic Theorem for uniformly convex Banach spaces

We provide an explicit uniform bound on the local stability of ergodic averages in uniformly convex Banach spaces. Our result can also be viewed as a finitary version in the sense of T. Tao of the Mean Ergodic Theorem for such spaces and so generalizes similar results obtained for Hilbert spaces by Avigad, Gerhardy and Towsner [1] and T. Tao [11].