INVESTIGADORES
CONDE Cristian Marcelo
artículos
Título:
A note about the norm of the sum and the anticommutator of two orthogonal projections
Autor/es:
CONDE, CRISTIAN
Revista:
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Editorial:
ACADEMIC PRESS INC ELSEVIER SCIENCE
Referencias:
Año: 2022 vol. 505
ISSN:
0022-247X
Resumen:
In this note, we prove that for any two orthogonal projections $P_mathcal{T}, P_mathcal{S}$ on a Hilbert the well-known normformulas $$|P_mathcal{T}+P_mathcal{S}|= 1+|P_mathcal{T}P_mathcal{S}|,$$ unless $P_mathcal{T}=P_mathcal{S}=0$and $$|P_{mathcal{T}}P_{mathcal{S}} + P_{mathcal{S}}P_{mathcal{T}}| = |P_{mathcal{T}}P_{mathcal{S}}|^2 +|P_{mathcal{T}}P_{mathcal{S}}|,$$ can be derived fromeach other. Such result is obtained from the relation between the spectra of the sum and product of any two idempotents in a Banach algebra. Applications of our results are given.
