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The Sasaki projection was introduced as a mapping from the lattice of closed subspaces of a Hilbert space onto one of its segments. To use this projection and its dual so-called Sasaki operations were introduced by the second two authors. In a previo
Externí odkaz:
http://arxiv.org/abs/2412.15764
Autor:
Chajda, Ivan, Länger, Helmut
The Sasaki projection and its dual were introduced as a mapping from the lattice of closed subspaces of a Hilbert space onto one of its segments. In a previous paper the authors showed that the Sasaki operations induced by the Sasaki projection and i
Externí odkaz:
http://arxiv.org/abs/2411.19347
Autor:
Chajda, Ivan, Länger, Helmut
We define a quasimodule Q over a bounded lattice L in an analogous way as a module over a semiring is defined. The essential difference is that L need not be distributive. Also for quasimodules there can be introduced the concepts of inner product, o
Externí odkaz:
http://arxiv.org/abs/2411.00730
Autor:
Chajda, Ivan, Länger, Helmut
By the operator of relative complementation is meant a mapping assigning to every element x of an interval [a,b] of a lattice L the set x^{ab} of all relative complements of x in [a,b]. Of course, if L is relatively complemented then x^{ab} is non-em
Externí odkaz:
http://arxiv.org/abs/2409.12291
Autor:
Chajda, Ivan, Länger, Helmut
The so-called Sasaki projection was introduced by U. Sasaki on the lattice L(H) of closed linear subspaces of a Hilbert space H as a projection of L(H) onto a certain sublattice of L(H). Since L(H) is an orthomodular lattice, the Sasaki projection an
Externí odkaz:
http://arxiv.org/abs/2408.03432
Not all logical systems can be captured using algebras. We see this in classical logic (formalized by Boolean algebras) and many-valued logics (like Lukasiewicz logic with MV-algebras). Even quantum mechanics, initially formalized with orthomodular l
Externí odkaz:
http://arxiv.org/abs/2406.20034
Autor:
Chajda, Ivan, Länger, Helmut
The present paper deals with complemented lattices where, however, a unary operation of complementation is not explicitly assumed. This means that an element can have several complements. The mapping $^+$ assigning to each element $a$ the set $a^+$ o
Externí odkaz:
http://arxiv.org/abs/2406.07665