Isomorphism of spaces of analytic functions on n-circular domains

The space A(D) of all analytic functions in a complete n-circular do- main D in Cn; n 2; is considered with a natural Fréchet topology. Some su¢ cient conditions for the isomorphism of such spaces are ob- tained in terms of certain subtle geometric characteristic of domains D. This investigation complements essentially the second authors result [8] on necessary geometric conditions of such isomorphisms

On lelong-bremermann lemma

The main theorem of this note is the following refinement of the well-known Lelong-Bremermann Lemma: Let u be a continuous plurisubharmonic function on a Stein manifold. of dimension n. Then there exists an integer m C-m, s = 1, 2,..., such that the sequence of functions u(s) (z) = 1/p(s) max (ln vertical bar g(j)((s)) (z)vertical bar : j = 1,..., m converges to u uniformly on each compact subset of Omega. In the case when Omega is a domain in the complex plane, it is shown that one can take m = 2 in the theorem above (Section 3); on the other hand, for n-circular plurisubharmonic functions in C-n the statement of this theorem is true with m = n + 1 (Section 4). The last section contains some remarks and open questions

On nuclearity of Köthe spaces

In this study we observe that the Köthe spaces Klp(A) is nuclear when it is complementedly embedded in Klq (B) for 1 p 2

On basis structure of power Köthe spaces of the first type

It is proved that Montel power Köthe spaces of the first type [5,8] have the structure of basis subspaces of the finite or infinite type invariant under isomorphisms, which strengthens authors’ previous results (joint with T. Terzioğlu) [18,19]. The main tools are special compound linear topological invariants, which evaluate classical geometric characteristic (namely inverse Bernstein diameters) of certain invariant multi-parameter constructions built from given bases of neighborhoods or bounded sets

Internal characteristics of domains in C-n

This paper is devoted to internal capacity characteristics of a domain D subset of C-n, relative to a point a is an element of D, which have their origin in the notion of the conformal radius of a simply Connected plane domain relative to a point. Our main goal is to study the internal Chebyshev constants and transfinite diameters for a domain D subset of C-n and its boundary partial derivative D relative to a point a is an element of D in the spirit of the author's article [Math. USSR-Sb. 25 (1975), 350-364], where similar characteristics have been investigated for compact sets in C-n. The central notion of directional Chebyshev constants is based on the asymptotic behavior of extremal monic "polynomials" and "copolynomials" in directions determined by the arithmetic of the index set Z(n). Some results are closely related to results on the sth Reiffen pseudometrics and internal directional analytic capacities of higher order (Jarnicki-Pflug, Nivoche) describing the asymptotic behavior of extremal "copolynomials" in varied directions when approaching the point a

Factorization of unbounded operators on Köthe spaces

The main result is that the existence of an unbounded continuous linear operator T between Kothe spaces lambda(A) and lambda(C) which factors through a third Kothe space A(B) causes the existence of an unbounded continuous quasidiagonal operator from lambda(A) into lambda(C) factoring through lambda(B) as a product of two continuous quasidiagonal operators. This fact is a factorized analogue of the Dragilev theorem [3, 6, 7, 2] about the quasidiagonal characterization of the relation (lambda(A), lambda(B)) is an element of B (which means that all continuous linear operators from lambda(A) to lambda(B) are bounded). The proof is based on the results of [9) where the bounded factorization property BF is characterized in the spirit of Vogt's [10] characterization of B. As an application, it is shown that the existence of an unbounded factorized operator for a triple of Kothe spaces, under some additonal asumptions, causes the existence of a common basic subspace at least for two of the spaces (this is a factorized analogue of the results for pairs [8, 2])