CDAM: Computational, Discrete and Applicable
Mathematics@LSE
CDAM Research Report, LSE-CDAM-2007-22
August 2007
CDAM: Computational, Discrete and Applicable
Mathematics@LSE
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CDAM Research Report, LSE-CDAM-2007-22August 2007 |
Stable Ranks of Banach Algebras of Operator-Valued H∞ Functions
Amol Sasane
Let E be an infinite-dimensional Hilbert space, and let H∞L(E) denote the Banach algebra of all functions f : D → L(E) that are holomorphic and bounded, equipped with the supremum norm |f|∞ := supz∈D |f(z)|L(E), f ∈ H∞L(E). We show that the Bass and topological stable ranks of H∞L(E) are infinite. If S is an open subset of T, then let ASL(E) denote the subalgebra of H∞L(E) of all functions that have a continuous extension to S. We also prove that ASL(E) has infinite Bass and topological stable ranks.A PDF file (128 kB) with the full contents of this report can be downloaded by clicking here.
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