منابع مشابه
On Unitarily Equivalent Submodules
The Hardy space on the unit ball in C provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n = 1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for modules over domains in C and for finitely-connected domains only for Hardy-like spaces, the bundle shifts. M...
متن کاملOn tridiagonal matrices unitarily equivalent to normal matrices
In this article the unitary equivalence transformation of normal matrices to tridiagonal form is studied. It is well-known that any matrix is unitarily equivalent to a tridiagonal matrix. In case of a normal matrix the resulting tridiagonal inherits a strong relation between its superand subdiagonal elements. The corresponding elements of the superand subdiagonal will have the same absolute val...
متن کاملFinite unions of submodules ON FINITE UNIONS OF SUBMODULES
This paper is concerned with finite unions of ideals and modules. The first main result is that if N ⊆ N1 ∪N2 ∪ · · · ∪Ns is a covering of a module N by submodules Ni, such that all but two of the Ni are intersections of strongly irreducible modules, then N ⊆ Nk for some k. The special case when N is a multiplication module is considered. The second main result generalizes earlier results on co...
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Let Gm,n be the Grassmann space of m-dimensional subspaces of F. Denote by θ1(X ,Y), . . . , θm(X ,Y) the canonical angles between subspaces X ,Y ∈ Gm,n. It is shown that Φ(θ1(X ,Y), . . . , θm(X ,Y)) defines a unitarily invariant metric on Gm,n for every symmetric gauge function Φ. This provides a wide class of new metrics on Gm,n. Some related results on perturbation and approximation of subs...
متن کاملOn the 2-absorbing Submodules
Let $R$ be a commutative ring and $M$ be an $R$-module. In this paper, we investigate some properties of 2-absorbing submodules of $M$. It is shown that $N$ is a 2-absorbing submodule of $M$ if and only if whenever $IJLsubseteq N$ for some ideals $I,J$ of R and a submodule $L$ of $M$, then $ILsubseteq N$ or $JLsubseteq N$ or $IJsubseteq N:_RM$. Also, if $N$ is a 2-absorbing submodule of ...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2008
ISSN: 0022-2518
DOI: 10.1512/iumj.2008.57.3406