Approximation by operators with fixed nullity

Bouldin, Richard

doi:10.1090/S0002-9939-1988-0938658-5

Approximation by operators with fixed nullity
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Proc. Amer. Math. Soc. 103 (1988), 141-144 Request permission

Abstract:

Let $T$ be a fixed operator on a complex separable Hilbert space $H$. The distance from $T$ to the operators with nullity equal to $n$, for each possible value of $n$, is determined.

References

Tsuyoshi Ando, Takashi Sekiguchi, and Teruo Suzuki, Approximation by positive operators, Math. Z. 131 (1973), 273–282. MR 320792, DOI 10.1007/BF01174903

Approximation of Hilbert space operators

Richard Bouldin, Positive approximants, Trans. Amer. Math. Soc. 177 (1973), 391–403. MR 317082, DOI 10.1090/S0002-9947-1973-0317082-6
Richard Bouldin, The essential minimum modulus, Indiana Univ. Math. J. 30 (1981), no. 4, 513–517. MR 620264, DOI 10.1512/iumj.1981.30.30042
John B. Conway, A course in functional analysis, Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1985. MR 768926, DOI 10.1007/978-1-4757-3828-5
Jacob Feldman and Richard V. Kadison, The closure of the regular operators in a ring of operators, Proc. Amer. Math. Soc. 5 (1954), 909–916. MR 68749, DOI 10.1090/S0002-9939-1954-0068749-2
P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887–933. MR 270173, DOI 10.1090/S0002-9904-1970-12502-2
P. R. Halmos, Positive approximants of operators, Indiana Univ. Math. J. 21 (1971/72), 951–960. MR 291829, DOI 10.1512/iumj.1972.21.21076
Saichi Izumino and Yoshinobu Kato, The closure of invertible operators on a Hilbert space, Acta Sci. Math. (Szeged) 49 (1985), no. 1-4, 321–327. MR 839947

Normal spectral approximation

Donald D. Rogers, Approximation by unitary and essentially unitary operators, Acta Sci. Math. (Szeged) 39 (1977), no. 1-2, 141–151. MR 448130
Pei Yuan Wu, Approximation by invertible and noninvertible operators, J. Approx. Theory 56 (1989), no. 3, 267–276. MR 990341, DOI 10.1016/0021-9045(89)90116-0