Embedding polydisk algebras into the disk algebra and an application to stable ranks
نویسندگان
چکیده
It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra A(D). As a consequence, one obtains uniform closed subalgebras of A(D) which have arbitrarily prescribed stable ranks.
منابع مشابه
Generalized essential norm of weighted composition operators on some uniform algebras of analytic functions
We compute the essential norm of a composition operator relatively to the class of Dunford-Pettis opertors or weakly compact operators, on some uniform algebras of analytic functions. Even in the frame of H∞ (resp. the disk algebra), this is new, as well for the polydisk algebras and the polyball algebras. This is a consequence of a general study of weighted composition operators.
متن کاملProduct preservation and stable units for reflections into idempotent subvarieties
We give a necessary and sufficient condition for the preservation of finite products by a reflection of a variety of universal algebras into an idempotent subvariety. It is also shown that simple and semi-left-exact reflections into subvarieties of universal algebras are the same. It then follows that a reflection of a variety of universal algebras into an idempotent subvariety has stable units...
متن کاملON THE USE OF KULSHAMMER TYPE INVARIANTS IN REPRESENTATION THEORY
Since 2005 a new powerful invariant of an algebra has emerged using the earlier work of Horvath, Hethelyi, Kulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. It was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...
متن کاملTHE MATRIX-VALUED Hp CORONA PROBLEM IN THE DISK AND POLYDISK
In this paper we consider the matrix-valued H corona problem in the disk and polydisk. The result for the disk is rather well known, and is usually obtained from the classical Carleson Corona Theorem by linear algebra. Our proof provides a streamlined way of obtaining this result and allows one to get a better estimate on the norm of the solution. In particular, we were able to improve the esti...
متن کاملTense like equality algebras
In this paper, first we define the notion of involutive operator on bounded involutive equality algebras and by using it, we introduce a new class of equality algebras that we called it a tense like equality algebra. Then we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between them, we prove that the tense ...
متن کامل