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Intersection properties of balls in spaces of compact operators

Asvald Lima (1978)

Annales de l'institut Fourier

We study the connection between intersection properties of balls and the existence of large faces of the unit ball in Banach spaces. Hanner’s result that a real space has the 3.2 intersection property if an only if disjoint faces of the unit ball are contained in parallel hyperplanes is extended to infinite dimensional spaces. It is shown that the space of compact operators from a space X to a space Y has the 3.2 intersection property if and only if X and Y have the 3.2 intersection property and...

Intersections of minimal prime ideals in the rings of continuous functions

Swapan Kumar Ghosh (2006)

Commentationes Mathematicae Universitatis Carolinae

A space X is called μ -compact by M. Mandelker if the intersection of all free maximal ideals of C ( X ) coincides with the ring C K ( X ) of all functions in C ( X ) with compact support. In this paper we introduce φ -compact and φ ' -compact spaces and we show that a space is μ -compact if and only if it is both φ -compact and φ ' -compact. We also establish that every space X admits a φ -compactification and a φ ' -compactification. Examples and counterexamples are given.

Intertwining Multiplication Operators on Function Spaces

Bahman Yousefi, Leila Bagheri (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Suppose that X is a Banach space of analytic functions on a plane domain Ω. We characterize the operators T that intertwine with the multiplication operators acting on X.

Intrinsic characterizations of distribution spaces on domains

V. Rychkov (1998)

Studia Mathematica

We give characterizations of Besov and Triebel-Lizorkin spaces B p q s ( Ω ) and F p q s ( Ω ) in smooth domains Ω ⊂ ℝ n via convolutions with compactly supported smooth kernels satisfying some moment conditions. The results for s ∈ ℝ, 0 < p,q ≤ ∞ are stated in terms of the mixed norm of a certain maximal function of a distribution. For s ∈ ℝ, 1 ≤ p ≤ ∞, 0 < q ≤ ∞ characterizations without use of maximal functions are also obtained.

Intrinsic geometric on the class of probability densities and exponential families.

Henryk Gzyl, Lázaro Recht (2007)

Publicacions Matemàtiques

We present a way of thinking of exponential farnilies as geodesic surfaces in the class of positive functions considered as a (multiplicative) sub-group G+ of the group G of all invertible elements in the algebra A of all complex bounded functions defined on a measurable space. For that we have to study a natural geometry on that algebra. The class D of densities with respect to a given rneasure will happen to be representatives of equivalence classes defining a projective space in A. The natural...

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