Note on K -analyticity and normality in function spaces

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Note on Normality in Qijasi-groups

An interesting problem in the theory of quasi-groups is to determine how strong an associative law must be assumed in order to obtain a theory of normal subquasi-groups similar to that of ordinary groups. The properties of normal subgroups which it is desirable to retain in the non-associative case are, first, that they form a Dedekind structure, and second, that each one gives rise to a quotie...

σ-Normality of Topological Spaces

A note on Volterra and Baire spaces

 In Proposition 2.6 in (G‎. ‎Gruenhage‎, ‎A‎. ‎Lutzer‎, ‎Baire and Volterra spaces‎, ‎textit{Proc‎. ‎Amer‎. ‎Math‎. ‎Soc.} {128} (2000)‎, ‎no‎. ‎10‎, ‎3115--3124) a condition that‎ ‎every point of $D$ is $G_delta$ in $X$ was overlooked‎. ‎So we‎ ‎proved some conditions by which a Baire space is equivalent to a‎ ‎Volterra space‎. ‎In this note we show that if $X$ is a‎ ‎monotonically normal $T_1...

A Note on Umd Spaces and Transference in Vector-valued Function Spaces

Abstract. A Banach space X is called an HT space if the Hilbert transform is bounded from L(X) into L(X), where 1 < p < ∞. We introduce the notion of an ACF Banach space, that is, a Banach space X for which we have an abstract M. Riesz Theorem for conjugate functions in L(X), 1 < p < ∞. Berkson, Gillespie, and Muhly [5] showed that X ∈ HT =⇒ X ∈ ACF. In this note, we will show that X ∈ ACF =⇒ X...