The Bass and Topological Stable Ranks of the Bohl Algebra Are Infinite
نویسندگان
چکیده
The Bohl algebra B is the ring of linear combinations of functions te on the real line, where k is any nonnegative integer, and λ is any complex number, with pointwise operations. We show that the Bass stable rank and the topological stable rank of B (where we use the topology of uniform convergence) are infinite.
منابع مشابه
Stable Ranks of Banach Algebras of Operator-valued H Functions
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 A S L(E) denote the subalgebra of H L(E) of all functions ...
متن کاملThe bass and topological stable ranks for algebras of almost periodic functions on the real line
Let Λ be a sub-semigroup of the reals. We show that the Bass and topological stable ranks of the algebras APΛ = {f ∈ AP : σ(f) ⊆ Λ} of almost periodic functions on the real line and with Bohr spectrum in Λ are infinite whenever the algebraic dimension of the Q-vector space generated by Λ is infinite. This extends Suárez’s result for APR = AP. Also considered are general subalgebras of AP. Intro...
متن کاملar X iv : 0 90 9 . 25 33 v 1 [ m at h . C V ] 1 4 Se p 20 09 TOPOLOGICAL STABLE RANK OF H ∞ ( Ω ) FOR CIRCULAR DOMAINS Ω
Let Ω be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by H(Ω) the Banach algebra of all bounded holomorphic functions on Ω, with pointwise operations and the supremum norm. We show that the topological stable rank of H(Ω) is equal to 2. The proof is based on Suarez’s theorem that the topological stable rank of H(D) is equal to 2, where D is t...
متن کاملTopological Stable Rank of H ∞ ( Ω ) for Circular Domains
— Let Ω be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by H(Ω) the Banach algebra of all bounded holomorphic functions on Ω, with pointwise operations and the supremum norm. We show that the topological stable rank of H(Ω) is equal to 2. The proof is based on Suarez’s theorem that the topological stable rank of H(D) is equal to 2, where D is...
متن کاملStable Ranks for the Sarason
We prove a Corona type theorem with bounds for the Sarason algebra H∞ + C and determine its spectral characteristics, thus continuing a line of research initiated by N. Nikolski. We also determine the Bass, the dense, and the topological stable ranks of H∞ + C. To fix our setting, let A be a commutative unital Banach algebra with unit e and M(A) its maximal ideal space. The following concept of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015