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Lines on projective varieties and applications

Francesco Russo
2011 Rendiconti del circolo matematico di Palermo  
The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.  ...  The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point.  ...  [Bǎ] and Corollary 2.4 here), implies the non-extendability of a lot of homogeneous varieties via the description of their Hilbert scheme of lines.  ... 
doi:10.1007/s12215-011-0072-0 fatcat:bmaqkeuk2jgrbjsxksrye3n2ju

Remark on two papers concerning axiomatics of quantum mechanics

Václav Alda
1980 Applications of Mathematics  
However, the Hilbert space constructed in [3] contains all states, not only the irreducible ones, and so it should be identified with the space of self-adjount operators A with tr (A 2 ) < co in the  ...  This correspondence can be extended linearly on to the linear space S£ generated by irreducible states so that the images belong to the space generated by observables and (1) 0 ^ <<p(S), o-> ^ 1 , SE^,  ... 
doi:10.21136/am.1980.103884 fatcat:wipytoigvfdgpjk5vjbi54texu

Page 683 of Mathematical Reviews Vol. 52, Issue 2 [page]

1976 Mathematical Reviews  
axiomatic approach to the number operator and its application to parastatistics.  ...  The irreducibility of the representations is achieved by using the little-group tech- nique and the scalar product for each irreducible Hilbert space is explicitly given.  ... 

Page 3991 of Mathematical Reviews Vol. , Issue 99f [page]

1999 Mathematical Reviews  
Recall that a (bounded linear) operator T on # is said to be irreducible if it does not commute with any nontrivial orthogonal projection, and strongly irreducible if it does not commute with any nontrivial  ...  A sufficient condition for such operators defined on Hilbert spaces to be extendible as operators of the same kind in Fréchet-Hilbert spaces is given.  ... 

Conservation laws in disordered electron systems: Thermodynamic limit and configurational averaging

V. Janiš, J. Kolorenč
2004 Physica status solidi. B, Basic research  
Mathematically this difficulty is manifested through the diffusion pole in the electron-hole irreducible vertex.  ...  We argue that although the norm of the electron wave function is conserved in individual realizations of the random potential, we cannot extend this conservation law easily to configurationally averaged  ...  These extended states are not proper vectors in the Hilbert space.  ... 
doi:10.1002/pssb.200404786 fatcat:qjcycxmg5ja4jk4wbueiorrtpe

Irreducibility of n-ary quantum information [article]

Karl Svozil
2001 arXiv   pre-print
Quantum information is radically different from classical information in that the quantum formalism (Hilbert space) makes necessary the introduction of irreducible "nits," n being an arbitrary natural  ...  ., [3, Footnote 6]), has not yet been acknowledged widely: the principal irreducibility of n-ary quantum information associated with the n-dimensionality of Hilbert space.  ...  As pointed out many times by Landauer and others (e.g., [1, 2] ) the formal concept of information is tied to physics, at least as far as applicability is a concern.  ... 
arXiv:quant-ph/0111113v1 fatcat:dxl2uo6cenenzlvercqoa5l5nu

Page 6870 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
Let A be a C*-algebra and let H be a Hilbert space that is infinite-dimensional and large enough for A.  ...  A result by Cowling and Steger states that z|I’ remains irreducible if 7m is not a discrete series representation and that z|I is determined by z.  ... 

Unitary Continuous Representations of Compact Quantum Groups [article]

Bernhard Drabant, Wolfgang Weich
1993 arXiv   pre-print
It is proved that the unitary continuous correpresentations decompose in finite dimensional irreducible correpresentations.  ...  on arbitrary Hilbert spaces.  ...  The antipode need not be continuous and can therefore not be extended on A.  ... 
arXiv:hep-th/9309053v1 fatcat:bla32wp7ejc73awv6zntifuev4

Page 1223 of Mathematical Reviews Vol. 38, Issue 6 [page]

1969 Mathematical Reviews  
The exponents k, and k, of a term cx":ys of this product determine a weight of an irreducible representation while the coefficient ¢ gives its multiplicity.  ...  , Berlin, 1964; MR 31 #6118; French translation, Dunod, Paris, 1967 ; MR 35 #7123] and topological algebras, and to their applications to physical systems.  ... 

Unique determination of an inner product by adjointness relations in the algebra of quantum observables

A D Rendall
1993 Classical and quantum gravity  
Some concrete examples are worked out in order to illustrate the meaning and range of applicability of the general theorems.  ...  It is shown that if a representation of a *-algebra on a vector space V is an irreducible *-representation with respect to some inner product on V then under appropriate technical conditions this property  ...  Acknowledgements I am grateful to Abhay Ashtekar and Jorma Louko for helpful discussions.  ... 
doi:10.1088/0264-9381/10/11/009 fatcat:ckmnzzu6mndglkoxuxdukybc6u

Page 8723 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
Summary: “This exposition collects some facts concerning the re- producing kernel Hilbert space and its multiplication operators and is oriented towards applications, especially to modelling un- bounded  ...  A continuous linear operator on a Hilbert space is said to be strongly irreducible if it does not have a pair of nontrivial, com- plementary invariant subspaces.  ... 

Page 147 of Mathematical Reviews Vol. 6, Issue 6 [page]

1945 Mathematical Reviews  
It follows that every isotope of a simple loop is simple. D. C. Murdoch (Vancouver, B. C.). Smiley, M. F. An application of lattice theory to quasi- groups. Bull. Amer. Math. Soc. 50, 782-786 (1944).  ...  mutually orthogonal finite dimensional subspaces invariant and _ irreducible under the group of operators U,.”"  ... 

An application of the DR-duality theory for compact groups to endomorphism categories of C*-algebras with nontrivial center [article]

Hellmut Baumgaertel, Fernando Lledo
2000 arXiv   pre-print
Furthermore, there is a natural equivalence relation between admissible subcategories and it is shown that two admissible subcategories yield A-module isomorphic Hilbert extensions iff they are equivalent  ...  Phys. 4 (1997) 785 we study Hilbert-C* systems F,G where the fixed point algebra A has nontrivial center Z and where A'∩ F=Z is satisfied.  ...  Irreducibility and decomposition theorem Since the C*-algebra A has a nontrivial center Z it is immediate that one needs to extend the notion of irreducible objects to the category T (cf. e.g.  ... 
arXiv:math/0012037v1 fatcat:hea7wz573zfoxd2652pzmmom3i

Integral representations for Markov transition probabilities

David G. Kendall
1958 Bulletin of the American Mathematical Society  
The following results (and one or two others like them) are proved in [3] ; the continuous-parameter analogues will appear in [4] and some applications will be discussed in [5].  ...  operators acting on a larger Hilbert space.  ...  operators acting on a larger Hilbert space.  ... 
doi:10.1090/s0002-9904-1958-10230-x fatcat:2xfuaa4lszdzfj3byuvlltuvki

Double-generic initial ideal and Hilbert scheme

Cristina Bertone, Francesca Cioffi, Margherita Roggero
2016 Annali di Matematica Pura ed Applicata  
a point of a given irreducible component, lower bounds for the number of irreducible components in a Hilbert scheme and the maximal Hilbert function in every irreducible component.  ...  Fogarty (1968) and R. Treger (1989).  ...  Acknowledgments The authors are grateful to Anthony Iarrobino for his generous suggestions and inspiring comments on the topic and the writing of this paper.  ... 
doi:10.1007/s10231-016-0560-0 fatcat:upaxybos5na5rfv5dpagi2arou
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