PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

Studia Mathematica

1997 | 125 | 2 | 187-199
Tytuł artykułu

Non-reflexive pentagon subspace lattices

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
On a complex separable (necessarily infinite-dimensional) Hilbert space H any three subspaces K, L and M satisfying K∩M = (0), K∨L = H and L⊂M give rise to what has been called by Halmos [4,5] a pentagon subspace lattice $P={(0),K,L,M,H}$. Then n = dim M ⊖ L is called the gap-dimension of P. Examples are given to show that, if n < ∞, the order-interval $[L,M]_{Lat Alg P} = {N ∈ Lat Alg P: L ⊆ N ⊆ M}$ in Lat Alg P can be either (i) a nest with n+1 elements, or (ii) an atomic Boolean algebra with n atoms, or (iii) the set of all subspaces of H between L and M. For n > 1, since Lat Alg P = P∩[L,M]_{Lat Alg P}\$, all such examples of pentagons are non-reflexive, the examples in case (iii) extremely so.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
187-199
Opis fizyczny
Daty
wydano
1997
otrzymano
1997-02-17
Twórcy
autor
• Department of Mathematics, University of Crete, Iraklion, Crete Greece
autor
• Department of Mathematics, The University of Western Australia, Nedlands, Western Australia 6907, Australia
Bibliografia
• [1] P. A. Fillmore and J. P. Williams, On operator ranges, Adv. Math. 7 (1971), 254-281.
• [2] E. Fischer, Intermediate Real Analysis, Springer, New York, 1983.
• [3] C. Foiaş, Invariant para-closed subspaces, Indiana Univ. Math. J. 21 (1972), 881-907.
• [4] P. R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76 (1970), 887-933.
• [5] P. R. Halmos, Reflexive lattices of subspaces, J. London Math. Soc. 4 (1971), 257-263.
• [6] W. E. Longstaff and P. Rosenthal, On two questions of Halmos concerning subspace lattices, Proc. Amer. Math. Soc. 75 (1979), 85-86.
• [7] E. Nordgren, M. Radjabalipour, H. Radjavi and P. Rosenthal, On invariant operator ranges, Trans. Amer. Math. Soc. 251 (1979), 389-398.
• [8] S.-C. Ong, Converse of a theorem of Foiaş and reflexive lattices of operator ranges, Indiana Univ. Math. J. 30 (1981), 57-63.
Typ dokumentu
Bibliografia
Identyfikatory