Abstract. By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic. We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently...

For a metric space (K, d) the Banach space Lip(K) consists of all scalar-valued bounded Lipschitz functions on K with the norm ‖f‖L = max(‖f‖∞, L(f)), where L(f) is the Lipschitz constant of f . The closed subspace lip(K) of Lip(K) contains all elements of Lip(K) satisfying the lip-condition lim0<d(x,y)→0 |f(x) − f(y)|/d(x, y) = 0. For K = ([0, 1], | · |), 0 < α < 1, we prove that lip(K) is a p...

We show how Ptak’s duality method leads to short proofs of two extensions of the Jordan canonical form, viz. the normal form for a matrix over an arbitrary (not necessarily algebraically closed) field under similarity and the canonical form for a pair of matrices under contragredient equivalence. The duality method is summarized in the following. Lemma. Let V be a finite-dimensional space over ...

An efficient Actionable 3D Subspace Clustering based on Optimal Centroids from continuous valued data represented three dimensionally which is suitable for real world problems profitable stocks discovery , biologically significant protein residues etc. It achieves actionable patterns ,incorporation of domain knowledge which allows users to choose the preferred utility(profit/benefit) function, ...

In this paper, we study domain-representable spaces, i.e., spaces that can be represented as the space of maximal elements of some continuous directed-complete partial order (= domain) with the Scott topology. We show that the Michael and Sorgenfrey lines are of this type, as is any subspace of any space of ordinals. We show that any completely regular space is a closed subset of some domainrep...

We study the intersection operation of closed linear subspaces in a separable Banach space. We show that if the ambient space is quasi-reflexive, then the intersection operation is Borel. On the other hand, if the space contains a closed subspace with a Schauder decomposition into infinitely many non-reflexive spaces, then the intersection operation is not Borel. As a corollary, for a closed su...

It is known that most subspace identification algorithms give biased estimates for closed-loop data due to a projection performed in the algorithms. In this work, consistency analysis of SIMPCA is given and the exact input requirement is formulated. The effect of column weighting in subspace identification algorithms is discussed and the column weighting for SIMPCA is designed which gives consi...

LetX be a complex Banach space andX∗ its dual space. We consider the topological subspace Π X { x, x∗ : x∗ x 1 ‖x‖ ‖x∗‖} of the product space BX ×BX∗ , equipped with norm and weak-∗ topology on the unit ball BX ofX and its dual unit ball BX∗ , respectively. It is easy to see that Π X is a closed subspace of BX × BX∗ . For two complex Banach spaces X and Y , denote by Cb BX : Y the Banach space ...

where M is a closed, compact, oriented Riemannian manifold, LM is the space of continuous maps from the circle into M–the free loop space of M–and C∗(LM) is the complex of singular chains on LM . Inspired by an idea in [6], chain-level string topology operations were constructed in [5] using a subspace of our space of string diagrams. This subspace • has a different homotopy type from the space...