Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $H^\infty$-functional calculus for commuting families of Ritt operators
  and sectorial operators   We introduce and investigate $H^\infty$-functional calculus for commuting
finite families of Ritt operators on Banach space $X$. We show that if either
$X$ is a Banach lattice or $X$ or $X^*$ has property $(\alpha)$, then a
commuting $d$-tuple $(T_1,\ldots, T_d)$ of Ritt operators on $X$ has an
$H^\infty$ joint functional calculus if and only if each $T_k$ admits an
$H^\infty$ functional calculus. Next for $p\in(1,\infty)$, we characterize
commuting $d$-tuple of Ritt operators on $L^p(\Omega)$ which admit an
$H^\infty$ joint functional calculus, by a joint dilation property. We also
obtain a similar characterisation for operators acting on a UMD Banach space
with property $(\alpha)$. Then we study commuting $d$-tuples $(T_1,\ldots,
T_d)$ of Ritt operators on Hilbert space. In particular we show that if $\Vert
T_k\Vert\leq 1$ for every $k=1,\ldots,d$, then $(T_1,\ldots, T_d)$ satisfies a
multivariable analogue of von Neumann's inequality. Further we show analogues
of most of the above results for commuting finite families of sectorial
operators.

21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph