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Observables and expectation on Pták's sum

In: Tatra Mountains Mathematical Publications, vol. 3, no. 2
Oľga Nánásiová
Detaily:
Rok, strany: 1993, 65 - 76
O článku:
A sum of a Boolean algebra and a quantum logic has been defined by P. Pták [P. Pták: Summing of Boolean algebras and logics, Demonstrat. Math. 19 (1986)] and is studied by V. Janiš, Z. Riečcanová [V. Janiš, Z. Riečanová: Completeness in sum of Boolean algebras and logic, Internat. J. Theoret. Phys. 31 (1992), 1689–1697], V. Janiš [V. Janiš: Notes on sums of Boolean algebras and logics, Demonstrat. Math. 23 (1990), 699–708], V. Janiš, O. Nánášiová [V. Janiš, O. Nánášiová: Pták's sum and direct products, Probastat'91, Bratislava 1991, 267–273], O. Nánášiová [O. Nánášiová: Homomorphism on the Pták's sum, Demonstrat. Math. 3-4 (1993)], [O. Nánášiová: States and homomorphism on the Pták's sum, Internat. J. Theoret. Phys. 32 (1993), 1957–1964], C. A. Drossos [C. A. Drossos: Boolean Methods and Pták's sum, preprint] etc. It was shown that there is a special case when this structure is a direct product [V. Janiš, Z. Riečanová: Completeness in sum of Boolean algebras and logic, Internat. J. Theoret. Phys. 31 (1992), 1689–1697], [V. Janiš, O. Nánášiová: Pták's sum and direct products, Probastat '91, Bratislava 1991, 267–273]. C. A. Drossos [C. A. Drossos: Boolean Methods and Pták's sum, preprint] has studied the connection between this structure and a bounded Boolean power. The sum is a free product iff the quantum logic is a Boolean algebra, too [O. Nánášiová: States and homomorphism on the Pták's sum, Internat. J. Theoret. Phys. 32 (1993), 1957–1964]. A representation of a state on Pták's sum with the function of conditional probability quantum logic is given. Further, we describe a conditional expectation of an observable on Pták's sum using the conditional expectation of an observable on the quantum logic with range in the center of the quantum logic. An example of this representation is given.
Ako citovať:
ISO 690:
Nánásiová, O. 1993. Observables and expectation on Pták's sum. In Tatra Mountains Mathematical Publications, vol. 3, no.2, pp. 65-76. 1210-3195.

APA:
Nánásiová, O. (1993). Observables and expectation on Pták's sum. Tatra Mountains Mathematical Publications, 3(2), 65-76. 1210-3195.