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Session 4. Banach Spaces and Operator Theory with Applications
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Asymptotic behaviour of factorization and projection constants |
Grzegorz Lewicki, Jagiellonian University, Kraków, Poland
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The talk is based on the joint work with Mieczysław Mastyło
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During this talk we present upper bounds of the Hilbertian norm of
projections on finite-dimensional subspaces of interpolation spaces
generated by certain abstract interpolation functors and show
applications to Calderón-Lozanovskii spaces. We prove estimates of
the \(p\)-factorization norm and projection constants for
finite-dimensional Banach lattices. We specialize our results to a
class of \(n\)-dimensional symmetric Banach spaces \(E_n\) and are
able to show that the projection constant \( \lambda(E_n)\) satisfy
\( \lim_{n \rightarrow \infty} \lambda(E_n)/\sqrt{n} =c,\) where \(
c = \sqrt{2/\pi}\) in the real case and \( c= \sqrt{\pi}/2\) in the
complex case.
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