image-subinvariant norms Original Research Article

Let image be a compact semigroup of operators on Fn, where F = R or F = C. A norm p on Fn is said to be image-subinvariant if image. If image is a closed subgroup of unitary operators on Fn the concept of image-subinvariant norm coincides with the concept of image-invariant norm studied in (C.K. Li, N.K. Tsing, Linear Algebra Appl. 150 (1991) 179–194). In this paper some basic properties of image-subinvariant norms are studied, and several results of Li and Tsing (C.K. Li, N.K. Tsing, Linear Algebra Appl. 150 (1991) 179–194) on group-invariant norms are extended to semigroup-subinvariant norms. As an application, necessary and sufficient conditions on a pair of vectors x, y set membership, variant Fn are obtained such that p(x) less-than-or-equals, slant p(y) holds for each weakly monotonic norm p.