Real and complex operator norms
| dc.creator | Holtz, Olga | |
| dc.creator | Karow, Michael | |
| dc.date | 2005-12-27 | |
| dc.date.accessioned | 2026-07-07T06:55:49Z | |
| dc.date.available | 2026-07-07T06:55:49Z | |
| dc.description | Real 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.description | 13 pages; manuscript, July 2004 | |
| dc.identifier | https://arxiv.org/abs/math/0512608 | |
| dc.identifier | http://arxiv.org/abs/math/0512608 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106406 | |
| dc.subject | Functional Analysis | |
| dc.subject | Rings and Algebras | |
| dc.subject | 47A30, 47B37, 47B38, 47B65, 46E30, 15A60, 15A04 | |
| dc.title | Real and complex operator norms | |
| dc.type | text |