Lipschitz Spaces and M -ideals
نویسنده
چکیده
For a metric space (K, d) the Banach space Lip(K) consists of all scalar-valued bounded Lipschitz functions on K with the norm ‖f‖L = max(‖f‖∞, L(f)), where L(f) is the Lipschitz constant of f . The closed subspace lip(K) of Lip(K) contains all elements of Lip(K) satisfying the lip-condition lim0<d(x,y)→0 |f(x) − f(y)|/d(x, y) = 0. For K = ([0, 1], | · |), 0 < α < 1, we prove that lip(K) is a proper M -ideal in a certain subspace of Lip(K) containing a copy of l∞.
منابع مشابه
Closed Ideals, Point Derivations and Weak Amenability of Extended Little Lipschitz Algebras
...
متن کاملOn the reducible $M$-ideals in Banach spaces
The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<infty)$, then the number of reducible $M$-ideals does not exceed of $frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The...
متن کاملCertain subalgebras of Lipschitz algebras of infinitely differentiable functions and their maximal ideal spaces
We study an interesting class of Banach function algebras of innitely dierentiable functions onperfect, compact plane sets. These algebras were introduced by Honary and Mahyar in 1999, calledLipschitz algebras of innitely dierentiable functions and denoted by Lip(X;M; ), where X is aperfect, compact plane set, M = fMng1n=0 is a sequence of positive numbers such that M0 = 1 and(m+n)!Mm+n ( m!Mm)...
متن کاملThe structure of ideals, point derivations, amenability and weak amenability of extended Lipschitz algebras
Let $(X,d)$ be a compactmetric space and let $K$ be a nonempty compact subset of $X$. Let $alpha in (0, 1]$ and let ${rm Lip}(X,K,d^ alpha)$ denote the Banach algebra of all continuous complex-valued functions $f$ on$X$ for which$$p_{(K,d^alpha)}(f)=sup{frac{|f(x)-f(y)|}{d^alpha(x,y)} : x,yin K , xneq y}
متن کاملCompact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions
We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.
متن کامل