Multipliers of the Hardy space H^1 and power bounded operators
| dc.creator | Pisier, Gilles | |
| dc.date | 2000-09-07 | |
| dc.date | 2000-12-26 | |
| dc.date.accessioned | 2026-07-07T04:37:15Z | |
| dc.date.available | 2026-07-07T04:37:15Z | |
| dc.description | We study the space of functions $ϕ\colon \NN\to \CC$ such that there is a Hilbert space $H$, a power bounded operator $T$ in $B(H)$ and vectors $ξ,η$ in $H$ such that $$ϕ(n) = < T^nξ,η>.$$ This implies that the matrix $(ϕ(i+j))_{i,j\ge 0}$ is a Schur multiplier of $B(\ell_2)$ or equivalently is in the space $(\ell_1 \buildrel {\vee}\over {\otimes} \ell_1)^*$. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach makes use of a new class of Fourier multipliers of $H^1$ which we call ``shift-bounded''. We show that there is a $ϕ$ which is a ``completely bounded'' multiplier of $H^1$, or equivalently for which $(ϕ(i+j))_{i,j\ge 0}$ is a bounded Schur multiplier of $B(\ell_2)$, but which is not ``shift-bounded'' on $H^1$. We also give a characterization of ``completely shift-bounded'' multipliers on $H^1$. | |
| dc.description | Submitted to Colloquium Math | |
| dc.identifier | https://arxiv.org/abs/math/0009074 | |
| dc.identifier | http://arxiv.org/abs/math/0009074 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59886 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 42B15, 47D03 | |
| dc.title | Multipliers of the Hardy space H^1 and power bounded operators | |
| dc.type | text |