In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable and locally finite CW complex L the following conditions are equivalent: L is quasi-finite. There exists a [L]-invertible mapping of a metrizable compactum X with e− dimX ≤ [L] onto the Hilbert cube. Finally, we construct an example of a quasi-finite complex L such that its extension type [...

In this paper we consider twelve classical laws of negation and study their relations in the context of BCKalgebras. A classification of the laws of negation is established and some characterizations are obtained. For example, using the concept of translation we obtain some characterizations of Hilbert algebras and commutative BCK-algebras with minimum. As a consequence we obtain a theorem rela...

Let A(D) be the disc algebra of all continuous complex-valued functions on the unit disc D holomorphic in its interior. Functions from A(D) act on the set of all contraction operators (‖A‖ 1) on Hilbert spaces. It is proved that the following classes of functions from A(D) coincide: (1) the class of operator Lipschitz functions on the unit circle T; (2) the class of operator Lipschitz functions...

Berele and Regev [1] defined the ring of hook Schur functions and showed that these functions are the characters of the general Lie superalgebra. Since the introduction of the hook Schur functions they have been extensively studied with respect to their combinatorial properties [2], [3], [4]. We compute the Hilbert series of this ring by giving a generating function for the partitions which fit...

We characterise imaginaries (up to interdefinability) in Hilbert spaces using a Galois theory for compact unitary groups.

We show several examples of n.a. valued fields with involution. Then, by means of a field of this kind, we introduce “n.a. Hilbert spaces” in which the norm comes from a certain hermitian sesquilinear form. We study these spaces and the algebra of bounded operators which are defined on them and have an adjoint. Essential differences with respect to the usual case are observed.

The reverse order laws for {1,3,4}-generalized inverses of a product of two operators have been studied by Wang et al. [J. Wang, H. Zhang, G. Ji, A generalized reverse order law for the products of two operators, Journal of Shaanxi Normal University, 38 (4) (2010), 13–17]. In this paper using a block-operator matrix technique we study mixed-type reverse-order laws for {1,3,4}-generalized invers...

The normal Moore space conjecture asserts that normal Moore spaces are metrizable. Nyikos has proven the consistency (from the existence of a strongly compact cardinal) of the conjecture holding and Fleissner has proven that at least a measurable cardinal is needed to prove the consistency. Although extremely elegant, Nyikos’ proof relies on Kunen’s proof of the consistency of the product measu...

We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was introduced by Székely, Rizzo and Bakirov, to general metric spaces. We show that for testing independence, it is necessary and sufficient that the metric space be of strong negative type. In particular, we show that this holds for separable Hilbert spaces, which answers a question of Kosorok. Instead of t...