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2 results

Integrated density of states for random metrics on manifolds
Daniel Lenz, Norbert Peyerimhoff, Ivan Veselić
Journal:

Proceedings of the London Mathematical Society / Volume 88 / Issue 3 / May 2004

Published online by Cambridge University Press:

14 April 2004, pp. 733-752

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May 2004
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We study ergodic random Schrödinger operators on a covering manifold, where the randomness enters both via the potential and the metric. We prove measurability of the random operators, almost sure constancy of their spectral properties, the existence of a self-averaging integrated density of states and a Pastur–šubin type trace formula.

Isometric Stability Property of Certain Banach Spaces
Alexander Koldobsky
Journal:

Canadian Mathematical Bulletin / Volume 38 / Issue 1 / 01 March 1995

Published online by Cambridge University Press:

20 November 2018, pp. 93-97

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01 March 1995
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Let E be one of the spaces C(K) and L1, F be an arbitrary Banach space, p > 1, and (X, σ) be a space with a finite measure. We prove that E is isometric to a subspace of the Lebesgue-Bochner space LP(X; F) only if E is isometric to a subspace of F. Moreover, every isometry T from E into Lp(X; F) has the form Te(x) = h(x)U(x)e, e ∊ E, where h: X —> R is a measurable function and, for every x ∊ X, U(x) is an isometry from E to F

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2 results

Integrated density of states for random metrics on manifolds

Isometric Stability Property of Certain Banach Spaces