Geodesic
Support projections on Banach spaces
Glasgow mathematical journal, Tome 18 (1977) no. 1, pp. 13-15

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Each bounded linear operator a on a Hilbert space K has a hermitian left-support projection p such that and (1 – p)K = ker α* = ker αα*. I demonstrate here that certain operators on Banach spaces also have left supports.Throughout this paper X will be a complex Banach space with norm-dual X', and L(X) will be the Banach algebra of bounded linear operators on X. Two linear subspaces Y and Z of X are orthogonal (in the sense of G. Birkhoff) if ∥ y ∥ ≦ ∥ y + z ∥ (y ∈Y, z ∈ Z); this orthogonality relation is not, in general, symmetric. It is easy to see that pX is orthogonal to (1 – p)X if and only if the norm of p is 0 or 1, when p is a projection on X. 
Spain, P. G. Support projections on Banach spaces. Glasgow mathematical journal, Tome 18 (1977) no. 1, pp. 13-15. doi: 10.1017/S0017089500002974
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[1] 1.Barnes, B. A., Representations of B*-algebras on Banach spaces, Pacific J. Math. 50 (1974), 7–18. Google Scholar | DOI

[2] 2.Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements of normed algebras (Cambridge U.P., 1971). Google Scholar | DOI

[3] 3.Bonsall, F. F. and Duncan, J., Numerical ranges II (Cambridge U.P., 1973). Google Scholar | DOI

[4] 4.Dunford, N. and Schwartz, J. T., Linear operators (Interscience, 1958, 1963, 1971). Google Scholar

[5] 5.Sakai, S., C*-algebras and W*-algebras (Springer-Verlag, 1971). Google Scholar

[6] 6.Sinclair, A. M., Eigenvalues in the boundary of the numerical range, Pacific J. Math. 35 (1970), 231–234. Google Scholar | DOI

[7] 7.Spain, P. G., On commutative K*-algebras II, Glasgow Math. J. 13 (1972), 129–134. Google Scholar | DOI

[8] 8.Spain, P. G., The W*-closure of a V*-algebra, J. London Math. Soc. (2) 7 (1973), 385–386. Google Scholar

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