Search

A Question of Valdivia on Quasinormable Fréchet Spaces
José Bonet
Journal:

Canadian Mathematical Bulletin / Volume 34 / Issue 3 / 01 September 1991

Published online by Cambridge University Press:

20 November 2018, pp. 301-304

Print publication:

01 September 1991
- Article
- - You have access
- PDF
- Export citation
It is proved that a Fréchet space is quasinormable if and only if every null sequence in the strong dual converges equicontinuously to the origin. This answers positively a question raised by Valdivia. As a consequence a positive answer to a problem of Jarchow on Fréchet Schwartz spaces is obtained.

A Note on Hardy-Orlicz Spaces
Zhang Jianzhong
Journal:

Canadian Mathematical Bulletin / Volume 33 / Issue 1 / 01 March 1990

Published online by Cambridge University Press:

20 November 2018, pp. 29-33

Print publication:

01 March 1990
- Article
- - You have access
- PDF
- Export citation
W. Deeb, R. Khalil and M. Marzuq have studied some properties of H(ϕ), the Hardy-Orlicz spaces. They introduced the functions class Np (0 < p ≦ 1 ) and discussed some properties of Np. In the present short note we prove that Np = N+ for 0 < p ≦ 1. We also give a condition of H(ϕ) = H(ψ).

A Remark on Complex Convexity*
Camino Leranoz
Journal:

Canadian Mathematical Bulletin / Volume 31 / Issue 3 / 01 September 1988

Published online by Cambridge University Press:

20 November 2018, pp. 322-324

Print publication:

01 September 1988
- Article
- - You have access
- PDF
- Export citation
We present a quasi-normed space which is locally H∞-convex but is not locally PL-convex in the sense of Davis, Garling and Tomczak-Jaegermann.

H(ϕ) Spaces
W. Deeb, M. Marzuq
Journal:

Canadian Mathematical Bulletin / Volume 29 / Issue 3 / 01 September 1986

Published online by Cambridge University Press:

20 November 2018, pp. 295-301

Print publication:

01 September 1986
- Article
- - You have access
- PDF
- Export citation
Let ψ be a non-decreasing continuous subadditive function defined on [0, ∞) and satisfy ψ(x) = 0 if and only if x = 0. The space H(ψ) is defined as the set of analytic functions in the unit disk which satisfy
and the space H+ (ψ) is the space of a f ∊ H(ψ) for which
where almost everywhere.
In this paper we study the H(ψ) spaces and characterize the continuous linear functionals on H+ (ψ).

Search Results