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- W1971296083 abstract "If $$mathcal{H}$$ is a Hilbert space, $$mathcal{S}$$ is a closed subspace of $$mathcal{H},$$ and A is a positive bounded linear operator on $$mathcal{H},$$ the spectral shorted operator $$rho left( {mathcal{S},mathcal{A}} right)$$ is defined as the infimum of the sequence $$sum (mathcal{S},A^n )^{1/n} ,$$ where denotes $$sum left( {mathcal{S},B} right)$$ the shorted operator of B to $$mathcal{S}.$$ We characterize the left spectral resolution of $$rho left( {mathcal{S},mathcal{A}} right)$$ and show several properties of this operator, particularly in the case that dim $${mathcal{S} = 1.}$$ We use these results to generalize the concept of Kolmogorov complexity for the infinite dimensional case and for non invertible operators." @default.
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- W1971296083 date "2005-12-20" @default.
- W1971296083 modified "2023-10-13" @default.
- W1971296083 title "Spectral Shorted Operators" @default.
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- W1971296083 doi "https://doi.org/10.1007/s00020-005-1382-4" @default.
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