Superstability of multipliers and ring derivations on Banach algebras.
We generalize to some classes of ultradifferentiable jets or functions the classical Łojasiewicz Division Theorem and Glaeser Composition Theorem. The proof uses the desingularization results by Hironaka, Bierstone and Milman.
Let A be a Banach *-algebra which is a subalgebra of a Banach algebra B. In this paper, assuming that A is symmetric, various conditions are given which imply that A is inverse closed in B.
Un -modulo hilbertiano destro su una -algebra dotato di uno -omomorfismo isometrico viene qui considerato come un oggetto della -categoria degli -moduli Hilbertiani destri. Come in [11], associamo ad esso una -algebra contenente come un «-bimodulo hilbertiano in ». Se è pieno e proiettivo finito è la -algebra , la generalizzazione delle algebre di Cuntz-Krieger introdotta da Pimsner [27] (e in un caso particolare da Katayama [31]). Più in generale, è canonicamente immersa...
It is a famous conjecture that every derivation on each Banach algebra leaves every primitive ideal of the algebra invariant. This conjecture is known to be true if, in addition, the derivation is assumed to be continuous. It is also known to be true if the algebra is commutative, in which case the derivation necessarily maps into the (Jacobson) radical. Because I. M. Singer and J. Wermer originally raised the question in 1955 for the case of commutative Banach algebras, the conjecture is...