3 research outputs found
On characterizations of a some classes of Schauder frames in Banach spaces
In this paper, we prove the following results. There exists a Banach space
without basis which has a Schauder frame. There exists an universal Banach
space (resp. ) with a basis (resp. an unconditional basis) such
that, a Banach has a Schauder frame (resp. an unconditional Schauder frame
) if and only if is isomorphic to a complemented subspace of (resp.
). For a weakly sequentially complete Banach space, a Schauder frame
is unconditional if and only if it is besselian. A separable Banach space
has a Schauder frame if and only if it has the bounded approximation property.
Consequenty, The Banach space of all
bounded linear operators on a Hilbert space has no Schauder
frame. Also, if and are Banach spaces with Schauder frames then, the
Banach space (the projective tensor product of
and ) has a Schauder frame. From the FaberSchauder system we construct a
Schauder frame for the Banach space (the Banach space of continuous
functions on the closed interval ) which is not a Schauder basis of
. Finally, we give a positive answer to some open problems related to
the Schauder bases (In the Schauder frames setting)
JACOBI TRANSFORM OF -JACOBI–LIPSCHITZ FUNCTIONS IN THE SPACE
Using a generalized translation operator, we obtain an analog of Younis' theorem [Theorem 5.2, Younis M.S. Fourier transforms of Dini–Lipschitz functions, Int. J. Math. Math. Sci., 1986] for the Jacobi transform for functions from the -Jacobi–Lipschitz class in the space