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We describe the geometrical structure on a complex quasi-Banach space $X$ that is necessay and sufficient for the existence of boundary limits for bounded, $X$ -valued analytic functions on the open unit disc of the complex plane. It is shown that in such spaces, closed bounded subsets have many plurisubharmonic barriers and that bounded upper semi-continuous functions on these sets have arbitrarily small plurisubharmonic perturbations that attain their maximum. This yields a certain representation of...

Points for symmetry of convex sets in the two-dimensional complex space - A counterexample to D. Yost's problem.

E. Behrends (1991)

Mathematische Annalen

Points of weak-norm continuity in the dual unit ball of injective tensor product spaces.

T.S.S.R.K. Rao (1999)

Collectanea Mathematica

In this note we exhibit points of weak*-norm continuity in the dual unit ball of the injective tensor product of two Banach spaces when one of them is a G-space.

Polar lattices from the point of view of nuclear spaces.

Wojciech Banaszczyk (1989)

Revista Matemática de la Universidad Complutense de Madrid

The aim of this survey article is to show certain questions concerning nuclear spaces and linear operators in normed spaces lead to questions from geometry of numbers.

Polynomial functions on the classical projective spaces

Yu. I. Lyubich, O. A. Shatalova (2005)

Studia Mathematica

The polynomial functions on a projective space over a field = ℝ, ℂ or ℍ come from the corresponding sphere via the Hopf fibration. The main theorem states that every polynomial function ϕ(x) of degree d is a linear combination of “elementary” functions ${| ⟨ x, \cdot ⟩ |}^{d}$ .

Polynomial inequalities in Banach spaces

Mirosław Baran (2015)

Banach Center Publications

We point out relations between the injective complexification of a real Banach space and polynomial inequalities. In particular we prove a generalization of a classical Szegő inequality to the case of polynomial mappings between Banach spaces. As an application we observe a complex version of known Bernstein-Szegő type inequalities.