595 research outputs found
Tensor product in symmetric function spaces
A concept of multiplicator of symmetric function space concerning to
projective tensor product is introduced and studied. This allows to obtain some
concrete results. In particular, the well-known theorem of R. O'Neil about the
boundedness of tensor product in the Lorentz spaces L_{p,q} is discussed.Comment: 17 page
A short proof of some recent results related to Ces{\`a}ro function spaces
We give a short proof of the recent results that, for every the Ces{\`a}ro function space is not a dual space, has the
weak Banach-Saks property and does not have the Radon-Nikodym property.Comment: 4 page
On uniqueness of distribution of a random variable whose independent copies span a subspace in L_p
Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes
of) p-integrable functions on [0,1]. It is known that a sequence of independent
copies of a mean zero random variable f from L_p spans in L_p a subspace
isomorphic to some Orlicz sequence space l_M. We present precise connections
between M and f and establish conditions under which the distribution of a
random variable f whose independent copies span l_M in L_p is essentially
unique.Comment: 14 pages, submitte
Interpolation of Ces{\`a}ro sequence and function spaces
The interpolation property of Ces{\`a}ro sequence and function spaces is
investigated. It is shown that is an interpolation space between
and for and with , where or
. The same result is true for Ces{\`a}ro sequence spaces. On the other
hand, is not an interpolation space between and
.Comment: 28 page
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