Real and complex operator norms

dc.creatorHoltz, Olga
dc.creatorKarow, Michael
dc.date2005-12-27
dc.date.accessioned2026-07-07T06:55:49Z
dc.date.available2026-07-07T06:55:49Z
dc.descriptionReal and complex norms of a linear operator acting on a normed complexified space are considered. Bounds on the ratio of these norms are given. The real and complex norms are shown to coincide for four classes of operators: 1) real linear operators from $L_p(μ_1)$ to $L_q(μ_2)$, $1\leq p\leq q\leq \infty$; 2) real linear operators between inner product spaces; 3) nonnegative linear operators acting between complexified function spaces with absolute and monotonic norms; 4) real linear operators from a complexified function space with a norm satisfying $\|\Re x \|\leq \|x\|$ to $L_\infty(μ)$. The inequality $p\leq q$ in Case 1 is shown to be sharp. A class of norm extensions from a real vector space to its complexification is constructed that preserve operator norms.
dc.description13 pages; manuscript, July 2004
dc.identifierhttps://arxiv.org/abs/math/0512608
dc.identifierhttp://arxiv.org/abs/math/0512608
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106406
dc.subjectFunctional Analysis
dc.subjectRings and Algebras
dc.subject47A30, 47B37, 47B38, 47B65, 46E30, 15A60, 15A04
dc.titleReal and complex operator norms
dc.typetext

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