Sur les isométries partielles maximales essentielles

Haïkel Skhiri

Studia Mathematica (1998)

  • Volume: 128, Issue: 2, page 135-144
  • ISSN: 0039-3223

Abstract

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We study the problem of approximation by the sets S + K(H), S e , V + K(H) and V e where H is a separable complex Hilbert space, K(H) is the ideal of compact operators, S = L ∈ B ( H ) : L * L = I is the set of isometries, V = S ∪ S* is the set of maximal partial isometries, S e = L ∈ B ( H ) : π ( L * ) π ( L ) = π ( I ) and V e = S e ∪ S e * where π : B(H) → B(H)/K(H) denotes the canonical projection. We also prove that all the relevant distances are attained. This implies that all these classes are closed and we remark that V e = V + K ( H ) . We also show that S + K(H) is both closed and open in S e . Finally, we prove that V e , S + K(H) and S e coincide with their boundaries ∂ ( V e ) , ∂(S + K(H)) and ∂ ( S e ) respectively.

How to cite

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Skhiri, Haïkel. "Sur les isométries partielles maximales essentielles." Studia Mathematica 128.2 (1998): 135-144. <http://eudml.org/doc/216479>.

@article{Skhiri1998,
author = {Skhiri, Haïkel},
journal = {Studia Mathematica},
keywords = {ideal of compact operators; set of isometries; set of maximal partial isometries; canonical projection},
language = {fre},
number = {2},
pages = {135-144},
title = {Sur les isométries partielles maximales essentielles},
url = {http://eudml.org/doc/216479},
volume = {128},
year = {1998},
}

TY - JOUR
AU - Skhiri, Haïkel
TI - Sur les isométries partielles maximales essentielles
JO - Studia Mathematica
PY - 1998
VL - 128
IS - 2
SP - 135
EP - 144
LA - fre
KW - ideal of compact operators; set of isometries; set of maximal partial isometries; canonical projection
UR - http://eudml.org/doc/216479
ER -

References

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