منابع مشابه
An Exotic Minimal Banach Space of Functions
This note describes a new Banach space B0 of square integrable functions on R having many interesting invariance properties. In fact, the Fourier transform, time-frequency shifts, and L-normalized dilations act isometrically on it. For its definition, we make use of a general construction principle for minimal invariant spaces. We demonstrate a variety of properties following immediately from t...
متن کاملOn certain equivalent norms on Tsirelson’s space
It remains open an important question as to whether or not there exists a distortable Banach space which is not arbitrarily distortable. The primary candidate for such a space is Tsirelson’s space T . While it is not difficult to directly define, for every 1 < λ < 2, an equivalent norm on T which is a λ-distortion, T does not belong to any general class of Banach spaces known to be arbitrarily ...
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 کاملDistorting Mixed Tsirelson Spaces∗
Any regular mixed Tsirelson space T (θn, Sn)IN for which θn θn → 0, where θ = limn θ n , is shown to be arbitrarily distortable. Certain asymptotic `1 constants for those and other mixed Tsirelson spaces are calculated. Also a combinatorial result on the Schreier families (Sα)α<ω1 is proved and an application is given to show that for every Banach space X with a basis (ei), the two ∆-spectrums ...
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: Israel Journal of Mathematics
سال: 1991
ISSN: 0021-2172,1565-8511
DOI: 10.1007/bf02782845