Approximate Diagonal Integral Representations and Eigenmeasures for Lipschitz Operators on Banach Spaces
نویسندگان
چکیده
A new stochastic approach for the approximation of (nonlinear) Lipschitz operators in normed spaces by their eigenvectors is shown. Different ways providing integral representations these approximations are proposed, depending on properties themselves whether they locally constant, (almost) linear, or convex. We use recently introduced notion eigenmeasure and focus attention procedures extending a function which known, to whole space. provide information natural error bounds, thus giving some tools measure what extent map can be considered diagonal with few errors. In particular, we show an approximate spectral theorem that verify certain convexity properties.
منابع مشابه
Linear operators of Banach spaces with range in Lipschitz algebras
In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.
متن کاملOn diagonal subdifferential operators in nonreflexive Banach spaces
Consider a real-valued bifunction f defined on C×C, where C is a closed and convex subset of a Banach space X , which is concave in its first argument and convex in its second one. We study its subdifferential with respect to the second argument, evaluated at pairs of the form (x, x), and the subdifferential of −f with respect to its first argument, evaluated at the same pairs. We prove that if...
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 کاملLipschitz - free Banach spaces
We show that when a linear quotient map to a separable Banach space X has a Lipschitz right inverse, then it has a linear right inverse. If a separable space X embeds isometrically into a Banach space Y , then Y contains an isometric linear copy of X. This is false for every nonseparable weakly compactly generated Banach space X. Canonical examples of nonseparable Banach spaces which are Lipsch...
متن کاملOn the Hardy-type Integral Operators in Banach Function Spaces
Characterization of the mapping properties such as boundedness, compactness, measure of non-compactness and estimates of the approximation numbers of Hardy-type integral operators in Banach function spaces are given.
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: Mathematics
سال: 2022
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math10020220