CDAM: Computational, Discrete and Applicable
CDAM Research Report, LSE-CDAM-2007-22
Stable Ranks of Banach Algebras of Operator-Valued H∞ Functions
Amol SasaneLet 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.
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