Maximum modulus theorems for algebras of operator valued functions
نویسندگان
چکیده
منابع مشابه
Carathéodory–Julia type theorems for operator valued Schur functions
We extend the Carathéodory–Julia theorem on angular derivatives as well as its higher order analogue established recently in [4] to the setting of contractive valued functions analytic on the unit disk. Carathéodory–Julia type conditions for an operator valued Schur-class function w are shown to be equivalent to the requirement that every function from the de Branges-Rovnyak space associated wi...
متن کاملStable 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 کاملModulus of convexity for operator convex functions
Most of the interesting examples deal with operators that are positive semi-definite. We shall follow the same convention in this paper. Operator convex functions are known to satisfy a number of interesting properties. An important discovery was made by Hansen and Pederson, who used Eq.1 in order to obtain an operator generalization of the Jensen inequality.[1] Recently, Effros provided an ele...
متن کاملOn the Structure of Maximum Modulus Algebras
i.e., if every fER attains its maximum modulus on C. As a matter of convenience, we shall, in this paper, abbreviate "maximum modulus algebra on K" to "ilf-algebra." Examples of Af-algebras which come to mind immediately are (a) the algebra ft consisting of all functions which are continuous on K and analytic in U, (b) any subalgebra of ft, (c) any algebra (B which is equivalent to an algebra o...
متن کاملDecomposition Theorems of Lie Operator Algebras
In this paper, we introduce a notion of Lie operator algebras which as a generalization of ordinary Lie algebras is an analogy of operator groups. We discuss some elementary properties of Lie operator algebras. Moreover, we also prove a decomposition theorem for Lie operator algebras.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1972
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1972.40.121