On Compact Perturbations of Operators
1974 ◽
Vol 26
(1)
◽
pp. 247-250
◽
Keyword(s):
Recently R. G. Douglas showed [4] that if V is a nonunitary isometry and U is a unitary operator (both acting on a complex, separable, infinite dimensional Hilbert space ), then V — K is unitarily equivalent to V ⊕ U (acting on ⊕ ) where K is a compact operator of arbitrarily small norm. In this note we shall prove a much more general theorem which seems to indicate "why" Douglas' theorem holds (and which yields Douglas' theorem as a corollary).
2020 ◽
Vol 369
◽
pp. 112561
2009 ◽
Vol 80
(1)
◽
pp. 83-90
◽
2005 ◽
Vol 79
(3)
◽
pp. 391-398
1966 ◽
Vol 18
◽
pp. 897-900
◽
1989 ◽
Vol 32
(3)
◽
pp. 320-326
◽
1996 ◽
Vol 37
(9)
◽
pp. 4203-4218
◽
2006 ◽
Vol 09
(02)
◽
pp. 305-314
◽
2006 ◽
Vol 13
(03)
◽
pp. 239-253
◽