Imbedding of power series spaces and spaces of analytic functions

Some Invariants of Frechet Spaces and Imbeddings of Smooth Sequence Spaces

“…Also much more important is the fact that there is a local imbedding of Aoo(!) into E [7]. This is a partial converse of the previous proposition and so the existence of a local imbedding can be formulated in this context in terms of the diametral dimension.…”

“…Although some new results are stated and proved in the present article, essentially they are modifications of the results of Aytuna, Krone and the author which are contained in [6] and [7]. …”

“…In §3, we show how we can also relate the existence of local imbeddings to some invariants like the diametral dimension, conditions (Illi..) and (n) of Vogt and Wagner [37] [44]. In this context, the concept of the "associated exponent sequence" introduced in [7] is also briefly discussed.…”

“…We begin by describing briefly what we have obtained in [6] and [7] about the linear-topological structure of the space of holomorphic functions on a Stein manifold. Some new results obtained by combining our results with the isomorphism theorem of Djakov [11] are also included.…”

“…One result which yields a true imbedding instead of a local one is 4.1. Theorem whose proof is given in [7].…”