منابع مشابه
On the character space of Banach vector-valued function algebras
Given a compact space $X$ and a commutative Banach algebra $A$, the character spaces of $A$-valued function algebras on $X$ are investigated. The class of natural $A$-valued function algebras, those whose characters can be described by means of characters of $A$ and point evaluation homomorphisms, is introduced and studied. For an admissible Banach $A$-valued function algebra...
متن کاملThe Banach Space
Let x be a sequence of real numbers and let p be a real number. The functor x yielding a sequence of real numbers is defined as follows: (Def. 1) For every natural number n holds x(n) = |x(n)|. Let p be a real number. Let us assume that p ≥ 1. The functor l yielding a non empty subset of the carrier of the linear space of real sequences is defined as follows: (Def. 2) For every set x holds x ∈ ...
متن کاملSome Banach Space Geometry
Notation. ε is an arbitrarily small positive number. L(X,Y ) is the Banach space of bounded linear operators T : X → Y . B(X) is the closed unit ball {x ∈ X : ‖x‖ 6 1}. N := N ∪ {∞} is the one-point compactification of the discrete space N. All operators are bounded and linear. A compact (topological) space always means a compact Hausdorff space. (We sometimes add “Hausdorff” explicitly for emp...
متن کاملA Hereditarily Indecomposable Asymptotic `2 Banach Space
A famous open problem in functional analysis is whether there exists a Banach space X such that every (bounded linear) operator on X has the form λ+K where λ is a scalar and K denotes a compact operator. This problem is usually called the “scalar-plus-compact” problem [14]. One of the reasons this problem has become so attractive is that by a result of N. Aronszajn and K.T. Smith [7], if a Bana...
متن کاملThe Daugavetian Index of a Banach Space
Given an infinite-dimensional Banach space X, we introduce the daugavetian index of X , daug (X), as the greatest constant m > 0 such that kId+ Tk > 1 +mkTk for all T ∈ K(X). We givetwo characterizations of this index and we estimate it in some examples. We show that the daugavetian index of a c0-, l1or l∞-sum of Banach spaces is the infimum index of the summands. Finally, we calculate the daug...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1965
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1965-0179607-4