C⁎-algebras, group algebras, and the algebra A(X) of approximable operators on a Banach space X having the bounded approximation property are known to be zero product determined. In this paper we ...give a quantitative estimate of this property by showing that, for the Banach algebra A, there exists a constant α with the property that for every continuous bilinear functional φ:A×A→C there exists a continuous linear functional ξ on A such thatsup‖a‖=‖b‖=1|φ(a,b)−ξ(ab)|≤αsup‖a‖=‖b‖=1,ab=0|φ(a,b)| in each of the following cases: (i) A is a C⁎-algebra, in which case α=8; (ii) A=L1(G) for a locally compact group G, in which case α=60271+sinπ101−2sinπ10; (iii) A=A(X) for a Banach space X having property (A) (which is a rather strong approximation property for X), in which case α=60271+sinπ101−2sinπ10C2, where C is a constant associated with the property (A) that we require for X.
ZERO JORDAN PRODUCT DETERMINED BANACH ALGEBRAS ALAMINOS, J.; BREŠAR, M.; EXTREMERA, J. ...
Journal of the Australian Mathematical Society (2001),
10/2021, Volume:
111, Issue:
2
Journal Article
Peer reviewed
Open access
A Banach algebra
$A$
is said to be a zero Jordan product determined Banach algebra if, for every Banach space
$X$
, every bilinear map
$\unicodeSTIX{x1D711}:A\times A\rightarrow X$
satisfying
...$\unicodeSTIX{x1D711}(a,b)=0$
whenever
$a$
,
$b\in A$
are such that
$ab+ba=0$
, is of the form
$\unicodeSTIX{x1D711}(a,b)=\unicodeSTIX{x1D70E}(ab+ba)$
for some continuous linear map
$\unicodeSTIX{x1D70E}$
. We show that all
$C^{\ast }$
-algebras and all group algebras
$L^{1}(G)$
of amenable locally compact groups have this property and also discuss some applications.
We consider several types of orthogonality conditions on the group algebra L1(G) of a locally compact group G such as f$\ast $g = 0, f$\ast $g☆ = 0, f☆$\ast $g = 0, f$\ast $g = g$\ast $f = 0 and ...f$\ast $g☆ = g☆$\ast $f = 0, and we describe the linear maps Φ: L1(G) → L1(H) between the group algebras of locally compact groups G and H that take orthogonal functions of L1(G) into orthogonal functions of L1(H). Roughly speaking, they are weighted homomorphisms in the case where we are concerned with the one-sided orthogonality conditions and weighted Jordan homomorphisms in the case where we treat the two-sided orthogonality conditions.
Atherosclerosis remains the leading cause of ischemic syndromes such as myocardial infarction or brain stroke, mainly promoted by plaque rupture and subsequent arterial blockade. Identification of ...vulnerable or high-risk plaques constitutes a major challenge, being necessary to identify patients at risk of occlusive events in order to provide them with appropriate therapies. Clinical imaging tools have allowed the identification of certain structural indicators of prone-rupture plaques, including a necrotic lipidic core, intimal and adventitial inflammation, extracellular matrix dysregulation, and smooth muscle cell depletion and micro-calcification. Additionally, alternative approaches focused on identifying molecular biomarkers of atherosclerosis have also been applied. Among them, proteomics has provided numerous protein markers currently investigated in clinical practice. In this regard, it is quite uncertain that a single molecule can describe plaque rupture, due to the complexity of the process itself. Therefore, it should be more accurate to consider a set of markers to define plaques at risk. Herein, we propose a selection of 76 proteins, from classical inflammatory to recently related markers, all of them identified in at least two proteomic studies analyzing unstable atherosclerotic plaques. Such panel could be used as a prognostic signature of plaque instability.
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•Atheroma plaque rupture is responsible of ischemic stroke and myocardial infarction.•It is compulsory to identify patients at risk to avoid such acute events.•A single marker cannot explain the complex process of plaque rupture.•Herein, a panel of protein markers related to plaque vulnerability is shown.
Let
(
K
,
d
)
be a non-empty, compact metric space and
α
∈
0
,
1
. Let
A be either
lip
α
(
K
)
or
Lip
α
(
K
)
and let
B be a commutative unital Banach algebra. We show that every continuous linear ...map
T
:
A
→
B
with the property that
T
(
f
)
T
(
g
)
=
0
whenever
f
,
g
∈
A
are such that
f
g
=
0
is of the form
T
=
w
Φ
for some invertible element
w in
B and some continuous epimorphism
Φ
:
A
→
B
.
Let A and B be C*-algebras, let X be an essential Banach A-bimodule and let T : A → B and S : A → X be continuous linear maps with T surjective. Suppose that T(a)T(b) + T(b)T(a) = 0 and S(a)b + bS(a) ...+ aS(b) + S(b)a = 0 whenever a, b ε A are such that ab = ba = 0. We prove that then T = wΦ and S = D + Ψ, where w lies in the centre of the multiplier algebra of B, Φ: A → B is a Jordan epimorphism, D: A → X is a derivation and Ψ: A → X is a bimodule homomorphism.
Abstract Endothelial progenitor cells (EPCs) constitute a promising alternative in cardiovascular regenerative medicine due to their assigned role in angiogenesis and vascular repair. In response to ...injury, EPCs promote vascular remodeling by replacement of damaged endothelial cells and/or by secreting angiogenic factors over the damaged tissue. Nevertheless, such mechanisms need to be further characterized. In the current approach we have evaluated the initial response of early EPCs (eEPCs) from healthy individuals after direct contact with the factors released by carotid arteries complicated with atherosclerotic plaques (AP), in order to understand the mechanisms underlying the neovascularization and remodeling properties assigned to these cells. Herein, we found that the AP secretome stimulated eEPCs proliferation and mobilization ex vivo , and such increase was accompanied by augmented permeability, cell contraction and also an increase of cell-cell adhesion in association with raised vinculin levels. Furthermore, a comparative mass spectrometry analysis of control versus stimulated eEPCs revealed a differential expression of proteins in the AP treated cells, mostly involved in cell migration, proliferation and vascular remodeling. Some of these protein changes were also detected in the eEPCs isolated from atherosclerotic patients compared to eEPCs from healthy donors. We have shown, for the first time, that the AP released factors activate eEPCs ex vivo by inducing their mobilization together with the expression of vasculogenic related markers. The present approach could be taken as a ex vivo model to study the initial activation of vascular cells in atherosclerosis and also to evaluate strategies looking to potentiate the mobilization of EPCs prior to clinical applications.
The main theorem states that a bounded linear operator $h$ from a unital $C^{\ast}$-algebra $A$ into a unital Banach algebra $B$ must be a homomorphism provided that $h(\bm{1})=\bm{1}$ and the ...following condition holds: if $x,y,z\in A$ are such that $xy=yz=0$, then $h(x)h(y)h(z)=0$. This theorem covers various known results; in particular it yields Johnson's theorem on local derivations.
•Practical segregation procedure to determine the g-function and borehole resistance.•It models the short-term of the ground heat exchanger behavior accurately.•Enhancement of a previous ...experiment-based short-term g-function study.•Auxiliary fluid and borehole thermal resistances are developed.•Method validated by a 3D numerical model and long-term simulations.
A detailed understanding of the short-term performance of the ground heat exchanger (GHE) is a major concern in the design of ground-source heat pumps (GSHP), as it has a significant impact in the efficiency and costs of the facility. The use of numerical models or artificial intelligence techniques may help in the short-term, although they are generally very time-consuming, becoming unpractical in numerous cases. The aim of this work is to obtain the thermal response factors according to the GHE, segregating the transient borehole behavior from the soil effect, based on a previous study which applies experimental data from thermal response tests (TRT) to the finite line source (FLS) model. The proposed method implies an extensive study of the fluid temperature as well as the development of new auxiliary thermal resistances related to the borehole and fluid, avoiding the implementation of numerical models. This procedure has been validated with the temperature outcomes of a 3D numerical model, obtaining low deviations, into a range of ±0.1 K, and mean absolute deviations below 0.01 K.
Let M be a von Neumann algebra, and let 0<p,q≤∞. Then the space HomM(Lp(M),Lq(M)) of all right M-module homomorphisms from Lp(M) to Lq(M) is a reflexive subspace of the space of all continuous linear ...maps from Lp(M) to Lq(M). Further, the space HomM(Lp(M),Lq(M)) is hyperreflexive in each of the following cases: (i) 1≤q<p≤∞; (ii) 1≤p,q≤∞ and M is injective, in which case the hyperreflexivity constant is at most 8.
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