Preservers of λ-Aluthge transforms Ben Ali Essaleh, Ahlem; Peralta, Antonio M.
Linear algebra and its applications,
10/2018, Volume:
554
Journal Article
Peer reviewed
Let M and N be arbitrary von Neumann algebras. For any a in M or in N, let Δλ(a) denote the λ-Aluthge transform of a. Suppose that M has no abelian direct summand. We prove that every bijective map ...Φ:M→N satisfyingΦ(Δλ(a∘b⁎))=Δλ(Φ(a)∘Φ(b)⁎), for all a,b∈M, (for a fixed λ∈0,1), maps the hermitian part of M onto the hermitian part of N (i.e. Φ(Msa)=Nsa) and its restriction Φ|Msa:Msa→Nsa is a Jordan isomorphism. If we also assume that Φ(x+iy)=Φ(x)+Φ(iy) for all x,y∈Msa, then there exists a central projection pc in M such that Φ|pcM is a complex linear Jordan ⁎-isomorphism and Φ|(1−pc)M is a conjugate linear Jordan ⁎-isomorphism.
Given two complex Hilbert spaces H and K with dim(H)≥2, we also show that every bijection Φ:B(H)→B(K) satisfyingΦ(Δλ(ab⁎))=Δλ(Φ(a)Φ(b)⁎), for all a,b∈B(H), must be a complex linear or a conjugate linear ⁎-isomorphism.
Let H be an infinite-dimensional complex Hilbert space and let G∞(H) be the set of all closed subspaces of H whose dimension and codimension both are infinite. We investigate (not necessarily ...surjective) transformations of G∞(H) sending every pair of subspaces to an equivalent pair of subspaces; two pairs of subspaces are equivalent if there is a linear isometry sending one of these pairs to the other. Let f be such a transformation. We show that there is up to a scalar multiple a unique linear or conjugate-linear isometry L:H→H such that for every X∈G∞(H) the image f(X) is the sum of L(X) and a certain closed subspace O(X) orthogonal to the range of L. In the case when H is separable, we give the following sufficient condition to assert that f is induced by a linear or conjugate-linear isometry: if O(X)=0 for a certain X∈G∞(H), then O(Y)=0 for all Y∈G∞(H).
Metallic conjugate connections Blaga, Adara M.; Hrețcanu, Cristina-Elena
Revista de la Unión Matemática Argentina,
06/2018
Journal Article
Peer reviewed
Open access
Properties of metallic conjugate connections are stated by pointing out their relation to product conjugate connections. We define the analogous in metallic geometry of the structural and the virtual ...tensors from the almost product geometry and express the metallic conjugate connections in terms of these tensors. From an applied point of view we consider invariant distributions with respect to the metallic structure and for a natural pair of complementary distributions, the above structural and virtual tensors are expressed in terms of O'Neill–Gray tensor fields.
The goal of this paper is to consider the notion of conjugate connection in a unifying setting for both almost complex and almost product geometries, having as model the works of Mileva Prvanović. A ...main interest is in finding classes of conjugate connections in duality with the initial linear connection; for example in the exponential case of almost complex geometry we arrive at a rule of quantization.
The Geometry of Product Conjugate Connections Blaga, Adara M.; Crăşmăreanu, Mircea
Analele ştiinţifice ale Universitatii "Al. I. Cuza" din Iaşi. Secţiunea 1a: Matematicǎ,
01/2013, Volume:
LIX, Issue:
1
Journal Article
Peer reviewed
Open access
Properties of pairs of product conjugate connections are stated with a special view towards the integrability of the given almost product structure. We define the analogous in product geometry of the ...structural and the virtual tensors from the Hermitian geometry and express the product conjugate connections in terms of these tensors. Some examples from the geometry of a pair of complementary distributions are discussed and for this case the above structural and virtual tensors are expressed in terms of O’Neill-Gray tensor fields.
This paper studies an enhanced widely linear (WL) receiver for direct-sequence code-division multiple-access (DS-CDMA) systems that employ aperiodic spreading sequences with offset quadrature ...phase-shift keying (OQPSK) modulation. The modulation scheme generates improper complex multiple-access interference (MAI) and necessitates the use of WL receivers. Focus is on bandlimited pulse shapes and the inherent cyclostationarity (CS) of the uncoded received signal. The enhanced WL receiver replaces the conventional chip-matched filter with new filters that exploit the CS of the received signal through frequency shifting. The proposed WL receiver is shown to outperform the classical strictly linear (SL) receiver when the interfering users are (quasi-)synchronous with respect to the user of interest. High-powered interfering users, that may exist to support high data rates, increase the performance improvement delivered by the WL receiver. Moreover, it is shown that MAI can become proper, either identically or asymptotically, when users are asynchronous and equally powered. This is despite the fact that individual interfering signals are improper. Numerical results demonstrate that the WL receiver can outperform the SL receiver by 1-3 dB under the examined scenarios with current CDMA standards settings. In asynchronous or quasi-synchronous transmission modes, performance gain of the WL receiver degrades unless the number of high-powered active users remains small. An example for implementation of the WL receiver is proposed and compared with that of the SL receiver when minimum-shift keying modulation, a special case of OQPSK, is used. The implementation is based on a fractionally spaced equalizer whose taps are updated by an adaptive algorithm. It is shown that the proposed structure is capable of delivering the maximum signal-to-noise ratio predicted by theory.
In this work, we prove that every Jordan
θ
-derivation is a
θ
-derivation. So we give an affirmative answer to a problem posed by C. Baak and M.S. Moslehian in the paper C. Baak and M.S. Moslehian, ...On the stability of
θ
-derivations on
J
B
∗
-triples, Bull. Braz. Math. Soc. 38 (1) (2007) 115–127.
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