Joint spectra
Joint spectra and multiplicative functionals
Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras [Book]
Joint spectral properties for permutable linear transformations.
Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces
Joint subnormality of a family of composition operators on L²-space is characterized by means of positive definiteness of appropriate Radon-Nikodym derivatives. Next, simplified positive definiteness conditions guaranteeing joint subnormality of a C₀-semigroup of composition operators are supplied. Finally, the Radon-Nikodym derivatives associated to a jointly subnormal C₀-semigroup of composition operators are shown to be the Laplace transforms of probability measures (modulo a C₀-group of scalars)...
Jordan isomorphisms and maps preserving spectra of certain operator products
Let ₁, ₂ be (not necessarily unital or closed) standard operator algebras on locally convex spaces X₁, X₂, respectively. For k ≥ 2, consider different products on elements in , which covers the usual product and the Jordan triple product T₁ ∗ T₂ = T₂T₁T₂. Let Φ: ₁ → ₂ be a (not necessarily linear) map satisfying whenever any one of ’s has rank at most one. It is shown that if the range of Φ contains all rank one and rank two operators then Φ must be a Jordan isomorphism multiplied by a root...
Julia's Lemma for Operators.
KAM theory in momentum space and quasiperiodic Schrödinger operators
Kato decomposition of linear pencils
T. Kato [5] found an important property of semi-Fredholm pencils, now called the Kato decomposition. M. A. Kaashoek [3] introduced operators having the property P(S:k) as a generalization of semi-Fredholm operators. In this work, we study this class of operators. We show that it is characterized by a Kato-type decomposition. Other properties are also proved.
Kato-Protter type inequalities, bounded vectors and the exponential function
K-Groups of Toeplitz Algebras of Reinhardt Domains.
Konstruktion von Operatoren und Kernen mit Hilfe von Absorptionsmengen.
Korovkin sets and mean ergodic theorems.
Korovkin theory in liminal JB-algebras.
Kreǐn's trace formula and the spectral shift function.
Krengel-Lin decomposition for noncompact groups
-boundedness and -compactness of a class of Fourier integral operators.
-Khintchine-Bonami inequality in free probability
We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length (). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.
bounds for spectral multipliers on rank one NA-groups with roots not all positive
We consider a family of non-unimodular rank one NA-groups with roots not all positive, and we show that on these groups there exists a distinguished left invariant sub-Laplacian which admits a differentiable functional calculus for every p ≥ 1.
L¹ factorizations, moment problems and invariant subspaces
For an absolutely continuous contraction T on a Hilbert space 𝓗, it is shown that the factorization of various classes of L¹ functions f by vectors x and y in 𝓗, in the sense that ⟨Tⁿx,y⟩ = f̂(-n) for n ≥ 0, implies the existence of invariant subspaces for T, or in some cases for rational functions of T. One of the main tools employed is the operator-valued Poisson kernel. Finally, a link is established between L¹ factorizations and the moment sequences studied in the Atzmon-Godefroy method, from...