Abstract
A linear space is a nonempty set L further defined by the following data:
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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
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1.
x + y = y + x;
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2.
(x + y) + z = x + (y + z);
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3.
There is an element 0 such that x + 0 = x for all x ∈ L;
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4.
For any x ∈ L there is an element x 1 such that x + x1 = 0.
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1.
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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:
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1.
α(x + y) = αx + αy;
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2.
(α + β)x = αx + βx;
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3.
(αβ)x = α(βx);
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4.
1 · x = x.
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1.
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© 1996 Birkhäuser Verlag
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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
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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
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