Recent Advances in Operator Theory and Operator Algebras
ثبت نشده
چکیده
In this article the spectral theorem for right linear compact normal operators on quaternionic Hilbert spaces is proved. Though the version of spectral theorem for such operators in quaternionic Hilbert space is appeared in recent literature using the left multiplication and considering the Hilbert space to be slice complex linear, we present a different approach, which is similar to the classical setup. In our method we do not use the left multiplication and work with single operator throughout. It is observed that the whole spherical spectrum of a compact normal operator is determined by the standard eigenvalues and deduce that the spherical spectrum of any n n quaternion matrix has exactly ncomplex eigenvalues. We illustrate our method with an example and compare it with that of the method given by Ghiloni etal. Rashmirekha Patra. Sambalpur University, India. Title: A result on Nijenhuis Operator. Abstract: Construction of Nijenhuis Operator on generalized Tangent bundle (TM ⊕ T ∗M) of a Differentiable manifold M and trivial deformation on its maximally isotropic subspace using Nijenhuis Operator has been done in the light of Dorfmann’s work. Pawel Pietrzycki. Jagiellonian University, Poland. Title: The equality C∗2C2 = (C∗C)2 is not sufficient for quasinormality of a composition operator C in L-space Abstract: It is proved that a closed densely defined operator C is quasinormali if and only if the equality C∗nCn = (C∗C)n holds for n = 2, 3. Let W be bounded injective weighted shift which satisfies the equality W ∗nW n = (W ∗W ). We prove that operator W is then quasinormal. We will construct examples of bounded, non-quasinormal operator C which satisfies equality C∗nCn = (C∗C)n. An example of such a operator is given in the class of weighted shifts on directed trees. What is important, the directed tree used in the construction is rootless and therefore the operator in example is unitarily equivalent to a composition operator in L-space. Marek Ptak. University of Agriculture in Krakow, Poland. Title: C-symmetric operators and its preanihilator
منابع مشابه
Positive Cone in $p$-Operator Projective Tensor Product of Fig`a-Talamanca-Herz Algebras
In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.
متن کاملSecond dual space of little $alpha$-Lipschitz vector-valued operator algebras
Let $(X,d)$ be an infinite compact metric space, let $(B,parallel . parallel)$ be a unital Banach space, and take $alpha in (0,1).$ In this work, at first we define the big and little $alpha$-Lipschitz vector-valued (B-valued) operator algebras, and consider the little $alpha$-lipschitz $B$-valued operator algebra, $lip_{alpha}(X,B)$. Then we characterize its second dual space.
متن کاملLie-type higher derivations on operator algebras
Motivated by the intensive and powerful works concerning additive mappings of operator algebras, we mainly study Lie-type higher derivations on operator algebras in the current work. It is shown that every Lie (triple-)higher derivation on some classical operator algebras is of standard form. The definition of Lie $n$-higher derivations on operator algebras and related pot...
متن کاملQuasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...
متن کاملPOWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES
The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014