Hilberträume mit amorphen basen

Norbert Brunner

Compositio Mathematica (1984)

  • Volume: 52, Issue: 3, page 381-387
  • ISSN: 0010-437X

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Brunner, Norbert. "Hilberträume mit amorphen basen." Compositio Mathematica 52.3 (1984): 381-387. <http://eudml.org/doc/89671>.

@article{Brunner1984,
author = {Brunner, Norbert},
journal = {Compositio Mathematica},
keywords = {Ramsey's theorem; weak form of the axiom of choice; existence of an amorphous set; every operator on a Hilbert space with an amorphous base is a direct sum of a finite matrix and a scalar operator},
language = {ger},
number = {3},
pages = {381-387},
publisher = {Martinus Nijhoff Publishers},
title = {Hilberträume mit amorphen basen},
url = {http://eudml.org/doc/89671},
volume = {52},
year = {1984},
}

TY - JOUR
AU - Brunner, Norbert
TI - Hilberträume mit amorphen basen
JO - Compositio Mathematica
PY - 1984
PB - Martinus Nijhoff Publishers
VL - 52
IS - 3
SP - 381
EP - 387
LA - ger
KW - Ramsey's theorem; weak form of the axiom of choice; existence of an amorphous set; every operator on a Hilbert space with an amorphous base is a direct sum of a finite matrix and a scalar operator
UR - http://eudml.org/doc/89671
ER -

References

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  1. [1] A.A. Albert and B. Muckenhoupt: Matrices of trace zero, Michigan Math. Journal4 (1957) 1-3. Zbl0077.24304MR83961
  2. [2] A. Blass: Ramsey's Theorem in the hierarchy of choice principles. Journal of Symbolic Logic42 (1977) 387-340. Zbl0374.02037MR465865
  3. [3] N. Brunner: Sequential Compactness and the Axiom of Choice. Notre Dame Journal of Formal Logic24 (1983) 89-92. Zbl0464.03045MR675919
  4. [4] N. Brunner: Dedekind-Endlichkeit und Wohlordenbarkeit, Monatshefte für Mathematik94 (1982) 9-31. Zbl0481.03030MR670012
  5. [5] J.W. Calkin: Two sided ideals in the ring of bounded operators. Ann. Math.42 (1941) 834-873. Zbl0063.00692MR5790
  6. [6] J. Cigler and H.C. Reichel: Topologie, Bibliograph. Inst. BI 121, Wien1978. Zbl0397.54001MR517542
  7. [7] N. Dunford and J.T. Schwartz: Linear Operators I Interscience, New York: (1957). Zbl0084.10402
  8. [8] J.L. Hickman: Groups in models of set theory, Bull. Aust. Math. Soc.14 (1976) 199-232. Zbl0324.02055MR409178
  9. [9] J.L. Hickman: Quasiminimal posets and lattices, Journal für die reine und angewandte Mathematik296 (1977) 10-13. Zbl0359.06003MR453521
  10. [10] T.J. Jech: The Axiom of ChoiceNew York: North Holland (1973) Zbl0259.02051MR396271
  11. [11] E.M. Kleinberg: The independence of Ramsey's theorem. Journal of Symbolic Logic34 (1969) 205-206. Zbl0185.01501MR255389
  12. [12] H. Läuchli: Auswahlaxiom in der Algebra. Commentarii Math. Helvetii37 (1963) 1-18. Zbl0108.01002MR143705
  13. [13] C. Pearcy: On the sum of two commutators. Proc. Amer. Math. Soc.16 (1959) 81-93. 
  14. [14] D. Pincus: The independence of the Boolean Prime Ideal theorem, Bull. Amer. Math. Soc.78 (1972) 766-770. Zbl0257.02051MR297565
  15. [15] J. Truss: Classes of Dedekind-Finite Cardinals. Fundamenta Math.84 (1974) 187-208. Zbl0292.02049MR469760
  16. [16] H. Wielandt: Unbeschränktheit der Operatoren der Quantenmechanik, Mathematische Annalen121 (1949) 21. Zbl0035.19903MR30701
  17. [17] A. Wintner: Unboundedness of Quantum Mechanical Matrices, Physical Rev.71 (1947) 738-739. Zbl0032.13602MR20724

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