2,356 research outputs found
Establishment of CP Violation in B Decays
No full textUntil recently, CP violation had been observed only in kaon decays. In order to conclusively interpret CP violation and test whether it can be explained in the framework of the Cabibbo-Kobayashi-Maskawa matrix, two asymmetric B factories, KEK-B and PEP-II, were constructed in the past decade. Recent measurements with the two detectors at these B factories clearly established large CP violation in neutral B mesons. We review the results and outline the prospects for future measurements
Browder spectral systems
No full textFor two spectral systems
σ
1
{\sigma _1}
and
σ
2
{\sigma _2}
on a Banach space
X
\mathcal {X}
, the associated Browder spectral system is
σ
b
;
1
,
2
:=
σ
1
∪
σ
2
′
{\sigma _{b;1,2}}: = {\sigma _1} \cup {\sigma ’_2}
. We prove that
σ
b
;
1
,
2
{\sigma _{b;1,2}}
possesses the projection and spectral mapping properties whenever
σ
1
{\sigma _1}
and
σ
2
{\sigma _2}
do (and satisfy a few additional mild assumptions). We also calculate
σ
b
;
1
,
2
{\sigma _{b;1,2}}
for tensor products. The results extend several previous works on Browder spectra.</p
The Browder spectrum of an elementary operator
No full textWe relate the ascent and descent of n-tuples of multiplication operators Ma,b(u)=aub to that of the coefficient Hilbert space operators a, b. For example, if a=(a1,…,an) and b∗=(b∗1,…,b∗m) have finite non-zero ascent and descent s and t, respectively, then the (n+m) -tuple (La,Rb) of left and right multiplication operators has finite ascent and descent s+t−1. . Using these results we obtain a description of the Browder joint spectrum of (La,Rb) and provide formulae for the Browder spectrum of an elementary operator acting on B(H) or on a norm ideal of B(H)
Onnewstrongversions of Browder type theorems
No full textAnoperator T actingonaBanachspace X satis estheproperty(UW )if a(T)∖ SF−
+
(T) = (T),
where a(T)istheapproximatepointspectrumofT, SF−
+
(T)istheuppersemi-WeylspectrumofT and (T)
the set of all poles of T. In this paper we introduce and study two new spectral properties, namely (V ) and
(V a
),inconnection with Browder type theorems introduced in [1], [2], [3] and [4]. Among other results, we
have that T satis es property (V ) if and only if T satis es property (UW ) and (T) = a(T).Estadística Aplicada y OptimizaciónMatemáticas aplicadasMateriales y EntornoQuímica y Física teóric
The upper browder spectrum in commutatively ordered banach algebras
No full textThesisA commutatively ordered Banach algebra (COBA) is a complex unital Banach
algebra A containing a subset C, called an algebra c-cone, such that C contains
the unit of A and is closed under addition, positive scalar multiplication and
multiplication by commuting positive elements. If the commutativity assumption
is removed, then the resulting cone is called an algebra cone. A Banach algebra
ordered by an algebra cone is called an ordered Banach algebra (OBA): Evidently,
every OBA is a COBA:
Not every COBA is however an OBA: An example con rming this statement is
given by the COBA (B(H);C); where B(H) is the space of all bounded linear
operators on a Hilbert space H and
C = fT 2 B(H) : hTx; xi 2 R+ for all x 2 Hg:
Benjamin and Mouton described Fredholm theory in OBAs relative to a homo-
morphism T : A ! B; where A and B are Banach algebras, and introduced an
element called an upper Browder element. An upper Browder element x 2 A is
an element of the form y + z; where y is invertible in A and z 2 C is an element
of the null space of T such that yz = zy: We denote by B+
T the set of all upper
Browder elements of A; which in turn gives (in a natural way) rise to the upper
Browder spectrum
+
T (x) := f 2 C : e �� x is not an upper Browder elementg:
In an OBA setting, Benjamin examined the following natural question: given
that the spectral radius of a positive element is not in the Fredholm spectrum of
the element, when will it be outside the upper Browder spectrum of that element?
The element satisfying this condition is said to have the upper Browder spectrum
property (see De nition 5.1.1). They went on to show that the connected hulls of
the upper Browder and the Browder spectra do not coincide in general, as well
as the conditions under which the upper Browder spectrum satisfy the spectral
mapping theorem.
In this study we extend these results to COBAs. Since every OBA is a COBA;
it is actually concluded that some results on upper Browder spectrum of an OBA
element readily extend to COBAs:
For further research, we recommend that the COBAs; rather than the OBAs;
should be the default setting for studying Fredholm theory
On property (Saw) and others spectral properties type Weyl-Browder theorems
No full textAn operator T acting on a Banach space X satisfies the property (aw) if σ(T) \ σw(T) = Ea(T), where σw(T) is the Weyl spectrum of T and Eo a(T) is the set of all eigenvalues of T of finite multiplicity that are isolated in the approximate point spectrum of T. In this paper we introduce and study two new spectral properties, namely (Saw) and (Sab), in connection with Weyl-Browder type theorems. Among other results, we prove that T satisfies property (Saw) if and only if T satisfies property (aw) and σSBF-+(T) = σw(T), where σSBF-+ (T) is the upper semi B-Weyl spectrum of T.Sanabria, José E.-713a9d59-342c-4562-b3d6-c06f5b214126-0Carpintero, Carlos R.-fe383790-b687-4109-8367-f91f6e274a1c-0Rosas Rodriguez, Ennis Rafael-0000-0001-8123-9344-600García, Orlando-3ec99ae8-85d0-4a8a-a21f-6cc390d93d03-
On new strong versions of Browder type theorems
No full textAn operator T acting on a Banach space X satisfies the property (UWπ) if σa(T)\σSF-+ (T) = π (T), where σa(T) is the approximate point spectrum of T, σSF-+ (T) is the upper semi-Weyl spectrum of T andπ (T) the set of all poles of T. In this paper we introduce and study two new spectral properties, namely (Vπ) and (Vπa ), in connection with Browder type theorems introduced in [1], [2], [3] and [4]. Among other results, we have that T satisfies property (Vπ) if and only if T satisfies property (UWπ) and π (T) = σa(T).Sanabria, José E.-713a9d59-342c-4562-b3d6-c06f5b214126-600Carpintero, Carlos R.-fe383790-b687-4109-8367-f91f6e274a1c-600Rodríguez, Jorge G.-418be70c-8b9f-40ad-9c18-a6df249a25bc-600Rosas, Ennis R.-93f330f4-73c5-435c-bbe0-40d8f6ffdac9-600García, Orlando-3ec99ae8-85d0-4a8a-a21f-6cc390d93d03-60
Sobre la propidedad (Saw) y otras propiedades espectrales tipo teoremas de Weyl-Browder
No full textAn operator T acting on a Banach space X satises the property (aw) if σ(T) \ σW(T) = E0a(T), where σW (T) is the Weyl spectrum of T and E0a(T) is the set of all eigenvalues of T of finite multiplicity that are isolated in the approximate point spectrum of T. In this paper we introduce and study two new spectral properties, namely (Saw) and (Sab), in connection with Weyl-Browder type theorems. Among other results, we prove that T satisfies property (Saw) if and only if T satisfies property (aw) and σSBF-+ (T) = σW (T), where σSBF-+ (T) is the upper semi B-Weyl spectrum of T.Un operador T actuando sobre un espacio de Banach X satisface la propiedad (aw) si σ(T) \ σW(T) = E0a(T), donde σW (T) es el espectro de Weyl de T y E0a(T) es el conjunto de todos los autovalores de T de multiplicidad finita que son aislados en el espectro aproximado puntual de T. En este artículo introducimos y estudiamos dos nuevas propiedades espectrales, llamadas (Saw) y (Sab), en conexión con teoremas tipo Weyl-Browder. Entre otros resultados, mostramos que T satisface la propiedad (Saw) si y sólo si T satisface la propiedad (aw) y σSBF-+ (T) = σW (T), donde σSBF-+ (T) es el espectro superiormente semi B-Weyl de T
Demiclosedness Principle and Convergence Theorems for Strictly Pseudocontractive Mappings of Browder–Petryshyn Type
No full textAbstractLet E be a real q-uniformly smooth Banach space which is also uniformly convex (for example, Lp or lp spaces, 1<p<∞) and K a nonempty closed convex subset of E. Let T:K→K be a strictly pseudocontractive mapping in the sense of F. E. Browder and W. V. Petryshyn (1967, J. Math. Anal. Appl.20, 197–228). It is proved that (I−T) is demiclosed at zero. If F(T)={x∈K:Tx=x}≠∅, weak and strong convergence of the Mann and Ishikawa iteration methods to a fixed point of T is proved
Brezis--Browder type results and representation formulae for s--harmonic functions
No full textIn this paper we prove Brezis--Browder type results for homogeneous fractional Sobolev spaces and quantitive type estimates for --harmonic functions. Such outcomes give sufficient conditions for a linear and continuous functional defined on to admit (up to a constant) an integral representation of its norm in terms of the Coulomb type energy and for distributional solutions of on to be of the form u(x)=\int_{\R^d}\frac{T(y)}{|x-y|^{d-2s}}dy+l, \quad l\in \R. $
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