Abstract
A linear space is a nonempty set L further defined by the following data:
-
A
To any pair of elements x ∈ L, y ∈ L there corresponds an element z called their sum and noted by x + y such that
-
1.
x + y = y + x;
-
2.
(x + y) + z = x + (y + z);
-
3.
There is an element 0 such that x + 0 = x for all x ∈ L;
-
4.
For any x ∈ L there is an element x 1 such that x + x1 = 0.
-
1.
-
B
To any element x ∈ L and each λ ∈ C there corresponds an element λ · x ∈ L such that for any x, y ∈ L, α, β ∈ C:
-
1.
α(x + y) = αx + αy;
-
2.
(α + β)x = αx + βx;
-
3.
(αβ)x = α(βx);
-
4.
1 · x = x.
-
1.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Birkhäuser Verlag
About this chapter
Cite this chapter
Egorov, Y., Kondratiev, V. (1996). Hilbert Spaces. In: On Spectral Theory of Elliptic Operators. Operator Theory Advances and Applications, vol 89. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9029-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-0348-9029-8_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9875-1
Online ISBN: 978-3-0348-9029-8
eBook Packages: Springer Book Archive