Let $\left(z_{\nu }\right)$ be a sequence in the upper half plane. If $1\<p\le \infty$ and if$$y_{\nu }^{1/p}f(z_{\nu })=a_{\nu },\nu =1,2,...(*)$$has solution $f\left(z\right)$ in the class of Poisson integrals of $L^p$ functions for any sequence $(a_{\nu })\in {\ell }^p$, then we show that $\left(z_{\nu }\right)$ is an interpolating sequence for $H^{\infty }$. If $f(z_{\nu })=a_{\nu }$, $\nu =1,2,...$ has solution in the class of Poisson integrals of BMO functions whenever $(a_{\nu })\in {\ell }^{\infty }$, then $\left(z_{\nu }\right)$ is again an interpolating sequence for $H^{\infty }$. A somewhat more general theorem is also proved and a counterexample for the case $p\le 1$ is described.

The classical Erdös spaces are obtained as the subspaces of real separable Hilbert space consisting of the points with all coordinates rational or all coordinates irrational, respectively. One can create variations by specifying in which set each coordinate is allowed to vary. We investigate the homogeneity of the resulting subspaces. Our two main results are: in case all coordinates are allowed to vary in the same set the subspace need not be homogeneous, and by specifying different sets for different...

We give a survey of our recent results on homological properties of Köthe algebras, with an emphasis on biprojectivity, biflatness, and homological dimension. Some new results on the approximate contractibility of Köthe algebras are also presented.

Extending previous results of H. Salas we obtain a characterisation of hypercyclic weighted shifts on an arbitrary F-sequence space in which the canonical unit vectors $\left(e_n\right)$ form a Schauder basis. If the basis is unconditional we give a characterisation of those hypercyclic weighted shifts that are even chaotic.

Let L be a normal Banach sequence space such that every element in L is the limit of its sections and let E = ind En be a separated inductive limit of the locally convex spaces. Then ind L(En) is a topological subspace of L(E).

Let ℓ be a Banach sequence space with a monotone norm $\parallel ·{\parallel }_{\ell }$, in which the canonical system $\left(e_i\right)$ is a normalized symmetric basis. We give a complete isomorphic classification of Cartesian products $E_0^{\ell }\left(a\right)\times E_{\infty }^{\ell }\left(b\right)$ where $E_0^{\ell }\left(a\right)=K^{\ell }\left(exp(-p^{-1}{a}_i)\right)$ and $E_{\infty }^{\ell }\left(b\right)=K^{\ell }\left(exp\left(p{a}_i\right)\right)$ are finite and infinite ℓ-power series spaces, respectively. This classification is the generalization of the results by Chalov et al. [Studia Math. 137 (1999)] and Djakov et al. [Michigan Math. J. 43 (1996)] by using the method of compound linear topological invariants developed by the third author....

Let Λ_R(α) be a nuclear power series space of finite or infinite type with lim_{j→∞} (1/j) log α_j = 0. We consider open polydiscs D_a in Λ_R(α)'_b with finite radii and the spaces H(D_a) of all holomorphic functions on D_a under the compact-open topology. We characterize all isomorphy classes of the spaces {H(D_a) | a ∈ Λ_R(α), a > 0}. In the case of a nuclear power series space Λ₁(α) of finite type we give this characterization in terms of the invariants (Ω̅ ) and (Ω̃ ) known from the theory...

We study those Köthe coechelon sequence spaces $k_p\left(V\right)$, 1 ≤ p ≤ ∞ or p = 0, which are locally convex (Riesz) algebras for pointwise multiplication. We characterize in terms of the matrix V = (vₙ)ₙ when an algebra $k_p\left(V\right)$ is unital, locally m-convex, a -algebra, has a continuous (quasi)-inverse, all entire functions act on it or some transcendental entire functions act on it. It is proved that all multiplicative functionals are continuous and a precise description of all regular and all degenerate maximal ideals...

In this paper, we show the representation of Köthe dual of Banach sequence spaces ${\ell }_p\left[X\right]$$(1\le p<\infty )...$

The isomorphic classification problem for the Köthe models of some $C^{\infty }$ function spaces is considered. By making use of some interpolative neighborhoods which are related to the linear topological invariant $D_{\phi }$ and other invariants related to the “quantity” characteristics of the space, a necessary condition for the isomorphism of two such spaces is proved. As applications, it is shown that some pairs of spaces which have the same interpolation property $D_{\phi }$ are not isomorphic.