TY - JOUR
T1 - p-Quasihyponormal operators have scalar extensions of order 6
AU - Ko, Eungil
N1 - Funding Information:
✩ This work was supported by a grant (R14-2003-006-01000-0) from Korea Research Foundation. E-mail address: eiko@ewha.ac.kr.
PY - 2007/6/1
Y1 - 2007/6/1
N2 - In this paper we show that every p-quasihyponormal operator has a scalar extension of order 6, i.e., is similar to the restriction to a closed invariant subspace of a scalar operator of order 6, where 0 < p < 1. As a corollary, we get that every p-quasihyponormal operator with rich spectra has a nontrivial invariant subspace. Also we show that Aluthge transforms preserve an analogue of the single-valued extension property for W2 (D, H) and an operator T.
AB - In this paper we show that every p-quasihyponormal operator has a scalar extension of order 6, i.e., is similar to the restriction to a closed invariant subspace of a scalar operator of order 6, where 0 < p < 1. As a corollary, we get that every p-quasihyponormal operator with rich spectra has a nontrivial invariant subspace. Also we show that Aluthge transforms preserve an analogue of the single-valued extension property for W2 (D, H) and an operator T.
KW - Invariant subspaces
KW - p-Quasihyponormal
KW - Scalar and subscalar operators
UR - http://www.scopus.com/inward/record.url?scp=33846911329&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2006.07.055
DO - 10.1016/j.jmaa.2006.07.055
M3 - Article
AN - SCOPUS:33846911329
SN - 0022-247X
VL - 330
SP - 80
EP - 90
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -