Abstract
If M and N are orthogonal subspaces of a Hilbert space, then M + N is closed (and therefore M + N = M ∨ N). Orthogonality may be too strong an assumption, but it is sufficient to ensure the conclusion. It is known that something is necessary; if no additional assumptions are made, then M + N need not be closed (see [50, p. 28], and Problems 52–55 below). Here is the conclusion under another very strong but frequently usable additional assumption.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Rights and permissions
Copyright information
© 1982 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Halmos, P.R. (1982). Spaces. In: A Hilbert Space Problem Book. Graduate Texts in Mathematics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9330-6_2
Download citation
DOI: https://doi.org/10.1007/978-1-4684-9330-6_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9332-0
Online ISBN: 978-1-4684-9330-6
eBook Packages: Springer Book Archive