The standard Brouwer-Zadeh poset Σ(H) is the poset of all effect operators on a Hilbert space H, naturally equipped with two types of orthocomplementation. In developing the theory, the question occured if (when) Σ(H ) fulfils the de Morgan property with respect to both orthocomplementation operations. In Ref. 3 the authors proved that it is the case provided dim H &lt; ∞, and they conjectured that if dim H = ∞, then the answer is in the negative. In this note, we first give a somewhat simpler proof of the known result for dim H &lt; ∞, and then we give a proof to the conjecture: We show that if dim H = ∞, then the de Morgan property is not valid

Cattaneo, G., Hamhalter, J., Ptack, P. (2000). On the de Morgan property of the standard Brouwer-Zadeh poset. FOUNDATIONS OF PHYSICS, 30(10), 1801-1805 [10.1023/A:1026414704133].

### On the de Morgan property of the standard Brouwer-Zadeh poset

#### Abstract

The standard Brouwer-Zadeh poset Σ(H) is the poset of all effect operators on a Hilbert space H, naturally equipped with two types of orthocomplementation. In developing the theory, the question occured if (when) Σ(H ) fulfils the de Morgan property with respect to both orthocomplementation operations. In Ref. 3 the authors proved that it is the case provided dim H < ∞, and they conjectured that if dim H = ∞, then the answer is in the negative. In this note, we first give a somewhat simpler proof of the known result for dim H < ∞, and then we give a proof to the conjecture: We show that if dim H = ∞, then the de Morgan property is not valid
##### Scheda breve Scheda completa Scheda completa (DC) Articolo in rivista - Articolo scientifico
de, morgan, property, standard, brouwer, zadeh, poset
English
2000
30
10
1801
1805
none
Cattaneo, G., Hamhalter, J., Ptack, P. (2000). On the de Morgan property of the standard Brouwer-Zadeh poset. FOUNDATIONS OF PHYSICS, 30(10), 1801-1805 [10.1023/A:1026414704133].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/20478`
##### Citazioni
• 0
• 0