In this paper, we introduce and study the mixed central bounded mean oscillation space , which is a new central version of the bounded mean oscillation spaces BMO. The pre-dual of is proved to be the ...mixed Herz–Hardy space . Moreover, we also give a characterization of via the boundedness of the commutators of n-dimensional Hardy operator and its dual operator on mixed Herz spaces .
This paper includes the new bounds that feature the vanishing generalized weighted Morrey spaces. In this regard, the article outlines the improved bounds about the class of fractional type rough ...higher order commutators on vanishing generalized weighted Morrey spaces.
Commutators on ℓ 1 Dosev, Detelin T.
Journal of functional analysis,
06/2009, Letnik:
256, Številka:
11
Journal Article
Recenzirano
Odprti dostop
The main result is that the commutators on
ℓ
1
are the operators not of the form
λ
I
+
K
with
λ
≠
0
and
K compact. We generalize Apostol's technique C. Apostol, Rev. Roumaine Math. Appl. 17 (1972) ...1513–1534 to obtain this result and use this generalization to obtain partial results about the commutators on spaces
X
which can be represented as
X
≃
(
⊕
i
=
0
∞
X
)
p
for some
1
⩽
p
<
∞
or
p
=
0
. In particular, it is shown that every compact operator on
L
1
is a commutator. A characterization of the commutators on
ℓ
p
1
⊕
ℓ
p
2
⊕
⋯
⊕
ℓ
p
n
is given. We also show that strictly singular operators on
ℓ
∞
are commutators.
Counterdiabatic (CD) driving presents a way of generating adiabatic dynamics at an arbitrary pace, where excitations due to nonadiabaticity are exactly compensated by adding an auxiliary driving term ...to the Hamiltonian. While this CD term is theoretically known and given by the adiabatic gauge potential, obtaining and implementing this potential in many-body systems is a formidable task, requiring knowledge of the spectral properties of the instantaneous Hamiltonians and control of highly nonlocal multibody interactions. We show how an approximate gauge potential can be systematically built up as a series of nested commutators, remaining well defined in the thermodynamic limit. Furthermore, the resulting CD driving protocols can be realized up to arbitrary order without leaving the available control space using tools from periodically driven (Floquet) systems. This is illustrated on few- and many-body quantum systems, where the resulting Floquet protocols significantly suppress dissipation and provide a drastic increase in fidelity.
For any formal commutator R of a free group F, we constructively prove the existence of a logical formula εr with the following properties. First, if we apply the collection process to a positive ...word W of the group F, then the structure of εr is determined by R, and the logical values of εr are determined by W and the arrangement of the collected commutators. Second, if the commutator R was collected during the collection process, then its exponent is equal to the number of elements of the set D(R) that satisfy εr, where D(R) is determined by R. We provide examples of εr for some commutators R and, as a consequence, calculate their exponents for different positive words of F. In particular, an explicit collection formula is obtained for the word (a1 ... an)m, n, m ≥ 1, in a group with the Abelian commutator subgroup. Also, we consider the dependence of the exponent of a commutator on the arrangement of the commutators collected during the collection process.
In this paper, we introduce and study maximal submultigroups and present some of its algebraic properties. Frattini submultigroups as an extension of Frattini subgroups is considered. A few ...submultigroups results on the new concepts in connection to normal, characteristic, commutator, abelian and center of a multigroup are established and the ideas of generating sets, fully and non-fully Frattini multigroups are presented with some significant results.
The Heisenberg-Robertson uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of ...their commutator. Notably, it does not capture the concept of incompatible observables because it can be trivial; i.e., the lower bound can be null even for two noncompatible observables. Here we give two stronger uncertainty relations, relating to the sum of variances, whose lower bound is guaranteed to be nontrivial whenever the two observables are incompatible on the state of the system.
In recent years, it has been well understood that a Calderón–Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse ...operators). We obtain a similar pointwise estimate for the commutator b,T with a locally integrable function b. This result is applied into two directions. If b∈BMO, we improve several weighted weak type bounds for b,T. If b belongs to the weighted BMO, we obtain a quantitative form of the two-weighted bound for b,T due to Bloom–Holmes–Lacey–Wick.
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