Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $H^{\infty}-$calculus and sums of closed operators   We develop a very general operator-valued functional calculus for operators
with an $H^{\infty}-$calculus. We then apply this to the joint functional
calculus of two commuting sectorial operators when one has an
$H^{\infty}$calculus. Using this we prove theorem of Dore-Venni type on sums of
commuting sectorial operators and apply our results to the problem of
$L_p-$maximal regularity. Our main assumption is the R-boundedness of certain
sets of operators, and therefore methods from the geometry of Banach spaces are
essential here. In the final section we exploit the special Banach space
structure of $L_1-$spaces and $C(K)-$spaces, to obtain some more detailed
results in this setting.

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The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: nucl-th