caa a22 4500 469043334 CHVBK 20180323132817.0 cr unu---uuuuu 170328e19921101xx s 000 0 eng 10.1007/BF01203126 doi (NATIONALLICENCE)springer-10.1007/BF01203126 Müller Vladimír Institute of Mathematics, Czechoslovak Academy of Sciences, Žitná 25, 115 67, Praha 1, Czechoslovakia aut On the essential approximate point spectrum of operators [Elektronische Daten] [Vladimír Müller] If λ belongs to the essential approximate point spectrum of a Banach space operatorT∈B(X) and $$\{ a_j \} _{j = 0}^\infty $$ is a sequence of positive numbers with lim j→∞ a j =0, then there existsx∈X such that $$\parallel p(T)x\parallel \geqslant a_{deg p} \left| {p(\lambda )} \right|$$ for every polynomialp. This result is the best possible — if $$\parallel p(T)x\parallel \geqslant c\left| {p(\lambda )} \right|$$ for some constantc>0 thenT has already a non-trivial invariant subspace, which is not true in general. Birkhäuser Verlag, 1992 Primary 47 A 53 nationallicence Secondary 47 A 15 nationallicence Integral Equations and Operator Theory Birkhäuser-Verlag 15/6(1992-11-01), 1033-1041 0378-620X 15:6<1033 1992 15 20 https://doi.org/10.1007/BF01203126 text/html Onlinezugriff via DOI 1 brief-communication jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01203126 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Müller Vladimír Institute of Mathematics, Czechoslovak Academy of Sciences, Žitná 25, 115 67, Praha 1, Czechoslovakia aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag 15/6(1992-11-01), 1033-1041 0378-620X 15:6<1033 1992 15 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer