Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal Block Tridiagonalization in B(H) and Beyond   For H a separable infinite dimensional complex Hilbert space, we prove that
every B(H) operator has a basis with respect to which its matrix representation
has a universal block tridiagonal form with block sizes given by a simple
exponential formula independent of the operator. From this, such a matrix
representation can be further sparsified to slightly sparser forms; it can lead
to a direct sum of even sparser forms reflecting in part some of its reducing
subspace structure; and in the case of operators without invariant subspaces
(if any exists), it gives a plethora of sparser block tridiagonal
representations. An extension to unbounded operators occurs for a certain
domain of definition condition. Moreover this process gives rise to many
different choices of block sizes.

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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys