Subscalar operators and growth of resolvent

被引:0
|
作者
Badea, Catalin [1 ]
Mueller, Vladimir
机构
[1] Univ Lille 1, CNRS, UMR 8524, Dept Math, F-59655 Villeneuve Dascq, France
[2] Acad Sci Czech Republ, Math Inst, Prague 11567 1, Czech Republic
关键词
subscalar operators; growth conditions; resolvents;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We construct a Banach space bounded linear operator T which is not epsilon(T)-subscalar but vertical bar vertical bar(T - z)(-1) vertical bar vertical bar <= (vertical bar z vertical bar - 1)(-1) for vertical bar z vertical bar > 1 and m(T - z) >= const.(1 - vertical bar z vertical bar)(3) for vertical bar z vertical bar < 1 (here m denotes the minimum modulus). This gives a negative answer to a variant of a problem of K.B. Laursen and M.M. Neumann. We also give a sufficient condition (in terms of growth of resolvent and of an analytic left inverse of T - z) implying that T is an epsilon(T)-subscalar operator. This condition is also necessary for Hilbert space operators.
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页码:249 / 258
页数:10
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