Every bounded self-ajoint operator is a real linear combination of $4$ orthoprojections

V. Rabanovich

Every bounded self-ajoint operator is a real linear combination of $4$ orthoprojections

Operator Algebras 2016-08-17 v1

Authors: V. Rabanovich

Abstract

We prove that every bounded self-adjoint operator in Hilbert space is a real linear combination of $4$ orthoprojections. Also we show that operators of the form identity minus compact positive operator can not be decomposed in a real linear combination of $3$ orthoprojections. Using ideas applied in infinite dimensional space, we find $n\times n$ matrices that are not real linear combinations of $3$ orthoprojections for every $n\ge 76$ .

Keywords

bounded self-adjoint operator orthoprojection real linear combination Hilbert space compact positive operator matrix decomposition

Cite

@article{arxiv.1608.04445,
  title  = {Every bounded self-ajoint operator is a real linear combination of $4$ orthoprojections},
  author = {V. Rabanovich},
  journal= {arXiv preprint arXiv:1608.04445},
  year   = {2016}
}

Comments

16 pages, A talk on conference: Groups and Operators, Gothenburg, Sweden, 2016

Every bounded self-ajoint operator is a real linear combination of $4$ orthoprojections

Abstract

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