Stable ranks of Banach algebras of operator-valued analytic functions
Sasane, A. J.
(2009).
Stable ranks of Banach algebras of operator-valued analytic functions.
Complex Analysis and Operator Theory,
3(1), 323-330.
https://doi.org/10.1007/s11785-008-0046-1
(2009).
Stable ranks of Banach algebras of operator-valued analytic functions.
Complex Analysis and Operator Theory,
3(1), 323-330.
https://doi.org/10.1007/s11785-008-0046-1
Let E be a separable infinite-dimensional Hilbert space, and let H(D; (E)) denote the algebra of all functions f:D (E) that are holomorphic. If is a subalgebra of H(D; (E)) , then using an algebraic result of Corach and Larotonda, we derive that under some conditions, the Bass stable rank of is infinite. In particular, we deduce that the Bass (and hence topological stable ranks) of the Hardy algebra H (D; (E)), the disk algebra A(D; (E)) and the Wiener algebra W+(D; (E)) are all infinite.