An exact Daugavet type inequality for small into isomorphisms in L 1期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

An exact Daugavet type inequality for small into isomorphisms in L 1

Authors:	M M Popov

Institution:	(1) Department of Applied Mathematics, Chernivtsi National University, str. Kotsiubyns’koho 2, Chernivtsi, 58012, Ukraine

Abstract:	The well known Daugavet property for the space L ₁ means that \|\| I + K \|\| = 1+ \|\| K \|\| for any weakly compact operator K : L ₁ → L ₁, where I is the identity operator in L ₁. We generalize this theorem to the case when we consider an into isomorphism J : L ₁ → L ₁ instead of I and a narrow operator T. Our main result states that $\parallel J +T\parallel \geq \parallel T\parallel \geq + \parallel J\parallel \left(\frac{2}{d} - 1\right)$ , where d = \|\| J\|\| \|\| J ⁻¹\|\|. We also give an example which shows that this estimate is exact. Received: 21 August 2007

Keywords:	Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 46B20 Secondary 47B38
本文献已被 SpringerLink 等数据库收录！