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Currently displaying 1 – 2 of 2

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On complex interpolation and spectral continuity

Karen Saxe — 1998

Studia Mathematica

Let ${[X_{0}, X_{1}]}_{t}$ , 0 ≤ t ≤ 1, be Banach spaces obtained via complex interpolation. With suitable hypotheses, linear operators T that act boundedly on both $X_{0}$ and $X_{1}$ will act boundedly on each ${[X_{0}, X_{1}]}_{t}$ . Let $T_{t}$ denote such an operator when considered on ${[X_{0}, X_{1}]}_{t}$ , and $σ (T_{t})$ denote its spectrum. We are motivated by the question of whether or not the map $t \to σ (T_{t})$ is continuous on (0,1); this question remains open. In this paper, we study continuity of two related maps: $t \to {(σ (T_{t}))}^{\land}$ (polynomially convex hull) and $t \to \partial_{e} (σ (T_{t}))$ (boundary of the polynomially convex...

Symmetric porosity of symmetric Cantor sets

Michael J. Evans; Paul D. Humke; Karen Saxe — 1994

Czechoslovak Mathematical Journal

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