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G-invariant norms and bicircular projections
Maja Fošner, Dijana Ilišević, Chi-Kwong Li, 2007, original scientific article

Abstract: It is shown that for many finite dimensional normed vector spaces ▫$V$▫ over ▫$Cc$▫, a linear projection ▫$P: V to V$▫ will have nice structure if ▫$P + lambda (I-P)$▫ is an isometry for some complex unit not equal to one. From these results, one can readily determine the structure of bicircular projections, i.e., those linear projections ▫$P$▫ such that ▫$P + mu (I - P)$▫ is an isometry for every complex unit ▫$mu$▫. The key ingredient in the proofs is the knowledge of the isometry group of the given norm. The proof techniques also apply to real vector spaces. In such cases, characterizations are given to linear projections ▫$P$▫ such that ▫$P - (I - P) = 2P - I$▫ is an isometry.
Keywords: bicircular projection, symmetric norms, unitarily invariant norms, unitary congruence invariant norms, unitary similarity invariant norms
Published: 10.07.2015; Views: 270; Downloads: 47
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