Some Hilbert Space Characterizations and Banach Space Inequalities
نویسندگان
چکیده
منابع مشابه
Banach and Hilbert Space Review
Definition 1.3 (Banach Spaces). It is easy to show that any convergent sequence in a normed linear space is a Cauchy sequence. However, it may or may not be true in an arbitrary normed linear space that all Cauchy sequences are convergent. A normed linear space X which does have the property that all Cauchy sequences are convergent is said to be complete. A complete normed linear space is calle...
متن کاملTest-space characterizations of some classes of Banach spaces
Let P be a class of Banach spaces and let T = {Tα}α∈A be a set of metric spaces. We say that T is a set of test-spaces for P if the following two conditions are equivalent: (1) X / ∈ P; (2) The spaces {Tα}α∈A admit uniformly bilipschitz embeddings into X. The first part of the paper is devoted to a simplification of the proof of the following test-space characterization obtained in M. I. Ostrov...
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 کاملSome Hilbert Space Extremal Problems
is achieved. This is given by e¡ = (1 -\-'Kkj)~1hj, where X is the unique positive root of £"-0 kj(l +\k])-1\hj\2 = M2. Davis proved the result by first considering the extremal problem for ra dimensional Euclidean space Rn. In this case the problem has the following geometric interpretation : (a") Let E be the hyperellipse {(oi, • • • , an): ]£?„„ kjOJ^M2} in Rn and suppose that h = (hi, • ■ ■...
متن کاملHermitian-Symmetric Inequalities in Hilbert Space
We establish several conditions which are equivalent to |[Bx, x]| ≤ 〈Ax, x〉 , ∀x ∈ H , where A is a nonnegative operator and B is a complex symmetric operator on a separable complex Hilbert space H. Along the way, we also prove a new factorization theorem for complex symmetric operators. Mathematics Subject Classification (2000). 47B99.
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: Mathematical Inequalities & Applications
سال: 1998
ISSN: 1331-4343
DOI: 10.7153/mia-01-09