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.

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ژورنال

عنوان ژورنال: Mathematics

سال: 2022

ISSN: ['2227-7390']

DOI: https://doi.org/10.3390/math10020220