Holomorphic semigroups in interpolation and extrapolation spaces.
Holomorphy types for open subsets of a Banach space
Homogeneous estimates for oscillatory integrals.
Hopf Extension Theorem of Measure
The authors have presented some articles about Lebesgue type integration theory. In our previous articles [12, 13, 26], we assumed that some σ-additive measure existed and that a function was measurable on that measure. However the existence of such a measure is not trivial. In general, because the construction of a finite additive measure is comparatively easy, to induce a σ-additive measure a finite additive measure is used. This is known as an E. Hopf's extension theorem of measure [15].
How far is C₀(Γ,X) with Γ discrete from C₀(K,X) spaces?
For a locally compact Hausdorff space K and a Banach space X we denote by C₀(K,X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Γ an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C₀(Γ,X) and C₀(K,X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur...
How far is C(ω) from the other C(K) spaces?
Let us denote by C(α) the classical Banach space C(K) when K is the interval of ordinals [1,α] endowed with the order topology. In the present paper, we give an answer to a 1960 Bessaga and Pełczyński question by providing tight bounds for the Banach-Mazur distance between C(ω) and any other C(K) space which is isomorphic to it. More precisely, we obtain lower bounds L(n,k) and upper bounds U(n,k) on d(C(ω),C(ωⁿk)) such that U(n,k) - L(n,k) < 2 for all 1 ≤ n, k < ω.
How small are the sets where the metric projection fails to be continuous
Hyers-Ulam constants of Hilbert spaces
The best constant in the Hyers-Ulam theorem on isometric approximation in Hilbert spaces is equal to the Jung constant of the space.
Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras.
Hypercyclic operators with an infinite dimensional closed subspace of periodic points.
Let X be an infinite dimensional separable Banach space. There exists a hypercyclic operator on X which is equal to the identity operator on an infinite dimensional closed subspace of X.
Hyperplane conjecture for quotient spaces of Lp.