Null spaces and ranges of polynomials of operators.
González, Manuel
Publicacions Matemàtiques, Tome 32 (1988), p. 167-170 / Harvested from Biblioteca Digital de Matemáticas
Access to full text

We give an elementary proof of the fact that given two polynomials P, Q without common zeros and a linear operator A, the operators P(A) and Q(A) verify some properties equivalent to the pair (P(A),Q(A)) being non-singular in the sense of J.L. Taylor. From these properties we derive expressions for the range and null space of P(A) and spectral mapping theorems for polynomials fo continuous (or closed) operators in Banach spaces.

Publié le : 1988-01-01
DMLE-ID : 3609 
@article{urn:eudml:doc:41050,
     title = {Null spaces and ranges of polynomials of operators.},
     journal = {Publicacions Matem\`atiques},
     volume = {32},
     year = {1988},
     pages = {167-170},
     zbl = {0669.47009},
     mrnumber = {MR0975895},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41050}
}

González, Manuel. Null spaces and ranges of polynomials of operators.. Publicacions Matemàtiques, Tome 32 (1988) pp. 167-170. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41050/