Literature Cited
D. Arlt, "Contractibility of general linear group of c0-space of null sequences," Invent. Math.,1, 36–44 (1966).
M. Atiyah, Lectures on K-Theory, Benjamin, New York-Amsterdam (1967).
K. Geba, "Fredholmσ-proper maps of Banach spaces," Fund. Math.,64, 341–373 (1969); especially, Appendix, 371–373.
I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators [in Russian], Nauka, Moscow (1965).
I. Ts. Gokhberg and M. G. Krein, Theory of Volterra Operators in Hilbert Space and Its Applications [in Russian], Nauka, Moscow (1967).
N. Dunford and J. Schwartz, Linear Operators (General Theory), Interscience Publishers, New York (1958).
R. C. James, "Bases and reflexivity of Banach spaces," Ann. Math.,52, 518–527 (1950).
R. C. James, "A non-reflexive Banach space isometric with its second conjugate space," Proc. Nat. Acad. Sci. USA,37, 174–177 (1951).
A. Douady, "A Banach space whose linear group is not connected," Indag. Math.,68, 787–789 (1965).
M. Day, Normed Linear Spaces, Springer, Berlin (1958).
S. Kwapien and A. Pelczynski, "The main triangle projection in matrix spaces and its applications," Studia Math.
N. H. Kuiper, "The homotopy type of the unitary group of Hilbert space," Topology,3, 19–30 (1965).
J. W. Milnor, "On spaces having the homotopy type of CW-complex," Trans. Amer. Math. Soc.,90, 272–280 (1959).
B. S. Mityagin, "Homotopic structure of linear group of Banach spaces," Uspekhi Mat. Nauk,25, No. 5 (1970).
G. Neubauer, "The homotopy type of the group of automorphisms in the spacesl p and c0," Math. Ann.,174, 33–40 (1967).
A. Pelczynski, "Projections in certain Banach spaces," Studia Math.,19, 209–228 (1960).
A. Pelczynski, "On strictly singular and strictly cosingular operators," Bull. Acad. Polon. Sci., ser. math.,13, No. 1, 31–41 (1965).
Z. Semadeni, "Banach space non-isomorphic to its square," II, Bull. Acad. Sci. Polon.,8, No. 2, 81–86 (1960).
I. Edelstein, B. Mitjagin, and E. Semenov, "The linear groups of C and L1 are contractible," Bull. Acad. Polon. Sci., ser. math.,18, No. 1, 27–33 (1970).
K. D. Elworthy, "Fredholm maps and GL(E)-structure," Bull. Amer. Math. Soc.,74, 582–587 (1968).
V. D. Mil'man, "A transformation of convex functions and the duality ofβ- andδ-characteristics," Dokl. Akad. Nauk SSSR,187, No. 1, 33–35 (1969).
V. D. Mil'man, "Studies in infinite-dimensional geometry of Banach spaces," Ph. D. Thesis, Khar'kov, FTINT AN UkrSSR (1969).
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Central Economic-Mathematical Institute of the Academy of Sciences of the USSR. Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 4, No. 3, pp. 61–72, July–September, 1970.
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Mityagini, B.S., Édel'shtein, I.S. Homotopy type of linear groups of two classes of Banach spaces. Funct Anal Its Appl 4, 221–231 (1970). https://doi.org/10.1007/BF01075242
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DOI: https://doi.org/10.1007/BF01075242