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Closed range weighted composition operators between lp-spaces

Lo Ching-on, Wai-keung Loh Anthony

Opuscula Mathematica

2021

Vol. 41, no. 5

649--665

We characterize the closedness of ranges of weighted composition operators between Lp-spaces, where 1 <≤ p ≤ ∞. When the Lp-spaces are weighted sequence spaces, several corollaries about this class of operators are also deduced.

A note on range-kernel uncomplementation

Kubrusly C., Duggal B. P.

Demonstratio Mathematica

2017

Vol. 50, nr 1

252--260

This note exhibits a Banach-space operator such that neither the range nor the kernel is complemented both for the operator and its adjoint.

Multiplication operators on weighted Banach spaces of analytic functions with exponential weights

Bogalska K.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

Vol. 49, no 4

409-416

Let v be the weight on the disc and M[phi] be the pointwise multiplication operator, M[phi](f) = [phi]f, on the weighted Banach space of analytic functions H[...](D) on the disc with the sup-norms. We characterize when M[phi] : H[...] --> H[...] is an isomorphism into for weights tending exponentially to zero at the boundary. In particular, the result holds for v(z) = exp[...] or v(z) = exp [...] for any [delta] > 0.