TY - JOUR
AU - Bermudez, T.
AU - Gonzalez, M.
T1 - On the boundedness of the local resolvent function
LA - eng
PY - 1999
SP - 1
EP - 8
T2 - Integral Equations and Operator Theory
SN - 0378-620X
VL - 34
IS - 1
PB - Birkhauser Verlag Basel
AB - For a hyponormal operator T on a complex Hilbert space H, we show that if the spectrum of T has empty interior, then the local resolvent function, cursive Greek chîT, is unbounded for every cursive Greek chi ∈ H \ {0}. In particular, if T is selfadjoint, then cursive Greek chîT is unbounded for every nonzero cursive Greek chi. The converse implication holds for a normal operator, but it is not true in general. Moreover, we give an example of an operator T in c0 whose spectrum has empty interior, but there exists a nonzero vector, cursive Greek chi, so that cursive Greek chîT is bounded.
DO - 10.1007/BF01332488
UR - https://portalciencia.ull.es/documentos/5e3adbe7299952629a024120
DP - Dialnet - Portal de la Investigación
ER -