Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A "typical" contraction is unitary   We show that (for the weak operator topology) the set of unitary operators on
a separable infinite-dimensional Hilbert space is residual in the set of all
contractions. The analogous result holds for isometries and the strong operator
topology as well. These results are applied to the problem of embedding
operators into strongly continuous semigroups.

14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin