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Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space

Kun Soo Chang, Dong Hyun Cho, Il Yoo (2004)

Czechoslovak Mathematical Journal

In this paper, we introduce a simple formula for conditional Wiener integrals over C 0 ( 𝔹 ) , the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on C 0 ( 𝔹 ) in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral...

Every separable L₁-predual is complemented in a C*-algebra

Wolfgang Lusky (2004)

Studia Mathematica

We show that every separable complex L₁-predual space X is contractively complemented in the CAR-algebra. As an application we deduce that the open unit ball of X is a bounded homogeneous symmetric domain.

Extendibility of polynomials and analytic functions on ℓ p

Daniel Carando (2001)

Studia Mathematica

We prove that extendible 2-homogeneous polynomials on spaces with cotype 2 are integral. This allows us to find examples of approximable non-extendible polynomials on ℓ p (1 ≤ p < ∞ ) of any degree. We also exhibit non-nuclear extendible polynomials for 4 < p < ∞. We study the extendibility of analytic functions on Banach spaces and show the existence of functions of infinite radius of convergence whose coefficients are finite type polynomials but which fail to be extendible.

Extending holomorphic maps in infinite dimensions

Bui Dac Tac (1991)

Annales Polonici Mathematici

Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results are known in...

Extension and lifting of weakly continuous polynomials

Raffaella Cilia, Joaquín M. Gutiérrez (2005)

Studia Mathematica

We show that a Banach space X is an ℒ₁-space (respectively, an ℒ ∞ -space) if and only if it has the lifting (respectively, the extension) property for polynomials which are weakly continuous on bounded sets. We also prove that X is an ℒ₁-space if and only if the space w b ( m X ) of m-homogeneous scalar-valued polynomials on X which are weakly continuous on bounded sets is an ℒ ∞ -space.

Extension of smooth functions in infinite dimensions, I: unions of convex sets

C. J. Atkin (2001)

Studia Mathematica

Let f be a smooth function defined on a finite union U of open convex sets in a locally convex Lindelöf space E. If, for every x ∈ U, the restriction of f to a suitable neighbourhood of x admits a smooth extension to the whole of E, then the restriction of f to a union of convex sets that is strictly smaller than U also admits a smooth extension to the whole of E.

Currently displaying 21 – 40 of 43