… In fact this is the general case: the Banach ball A in Theorem … of a well-chosen Banach space
of holomorphic functions. … A family (X, π, A, Φ) we shall often also call an analytic family of …

… , whose values are in a Banach space, having such a power series developments is called
analytic, Then, the theorem reads: If [r(z)] is analytic for each in the dual space, r is analytic. …

… a Banach space X such that X ∗ has neither a w ∗ -N-family … In [4] it is proved that a Banach
space X fails to have a copy … ∗ -compact subset of X ∗ and every w ∗ -K analytic boundary …

… Banach space, we write X* for the dual space and Bx for the closed unit ball of X. We use
brackets ( , ) for the pairing between a Banach space … Some of the Banach space ideas used in …

… Thus, applying the usual functionalanalytic constructions (with … Banach spaces having
two module structures let us shortly recall some definitions and basic facts concerning Banach …

… of complete metric spaces) and hence a Banach space. In particular, … Banach spaces are
themselves Banach spaces. Before proceeding to our next specific example of a Banach space…

… The remainder of the chapter is concerned with metric spaces, some more general analytic
… results on analytic functions are vitally needed in the theory of complex Banach algebras. It is …

… basis in a Banach space is very desirable. Bases are not only very useful in many analytic
calculations and various constructions but can also be used to classify Banach spaces. The …

… , analytic functions and … -Banach spaces. Many of the results and problems in this section
are interesting in the category of F-spaces but we will restrict ourselves to quasi-Banach spaces …

… and their application to the Fourier analysis of functions having values in a Banach space. …
for every Banach space B? We can show that at least for many of the classical Banach spaces …