Transactions of the American Mathematical Society
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A divergence theorem for Hilbert space
Transactions of the American Mathematical Society - Tập 164 Số 0 - Trang 411-426
Let B be a real separable Banach space. A suitable linear imbedding of a real
separable Hilbert space into B with dense range determines a probability measure
on B which is known as abstract Wiener measure. In this paper it is shown that
certain submanifolds of B carry a surface measure uniquely defined in terms of
abstract Wiener measure. In addition, an identity is obtained which relates
surface...
The Boolean space of orderings of a field
Transactions of the American Mathematical Society - Tập 209 Số 0 - Trang 225-235
It has been pointed out by Knebusch, Rosenberg and Ware that the set X X of all
orderings on a formally real field can be topologized to make a Boolean space
(compact, Hausdorff and totally disconnected). They have called the sets of
orderings W ( a ) = { > in X | a > 0 } W(a) = \{ > {\text { in }}X|a > 0\} the
Harrison subbasis of X X . This subbasis is closed under symmetric difference
and com...
Isometric dilations for infinite sequences of noncommuting operators
Transactions of the American Mathematical Society - Tập 316 Số 2 - Trang 523-536
This paper develops a dilation theory for { T n } n = 1 ∞ \{ {T_n}\} _{n =
1}^\infty an infinite sequence of noncommuting operators on a Hilbert space,
when the matrix [ T 1 , T 2 , … ] [{T_1},{T_2}, \ldots ] is a contraction. A
Wold decomposition for an infinite sequence of isometries with orthogonal final
spaces and a minimal isometric dilation for { T n } n = 1 ∞ \{ {T_n}\} _{n =
1}^\infty are ...
A decomposition for combinatorial geometries
Transactions of the American Mathematical Society - Tập 171 Số 0 - Trang 235-282
A construction based on work by Tutte and Grothendieck is applied to a
decomposition on combinatorial pregeometries in order to study an important
class of invariants. The properties of this Tutte decomposition of a pregeometry
into a subgeometry G ∖ e G\backslash e and contraction G / e G/e is explored in
a categorically integrated view using factored strong maps. After showing that
direct sum de...
Torsion free and projective modules
Transactions of the American Mathematical Society - Tập 102 Số 2 - Trang 319-327
Geometric consequences of extremal behavior in a theorem of Macaulay
Transactions of the American Mathematical Society - Tập 346 Số 1 - Trang 203-235
F. S. Macaulay gave necessary and sufficient conditions on the growth of a
nonnegative integer-valued function which determine when such a function can be
the Hilbert function of a standard graded k k -algebra. We investigate some
algebraic and geometric consequences which arise from the extremal cases of
Macaulay’s theorem. Our work also builds on the fundamental work of G. Gotzmann.
Our principa...
Primitive satisfaction and equational problems for lattices and other algebras
Transactions of the American Mathematical Society - Tập 190 Số 0 - Trang 125-150
This paper presents a general method of solving equational problems in all
equational classes of algebras whose congruence lattices are distributive, such
as those consisting of lattices, relation algebras, cylindric algebras,
orthomodular lattices, lattice-ordered rings, lattice-ordered groups, Heyting
algebras, other lattice-ordered algebras, implication algebras, arithmetic
rings, and arithmeti...
Equational bases and nonmodular lattice varieties
Transactions of the American Mathematical Society - Tập 174 - Trang 1-1 - 1972
Oscillatory properties of certain nonlinear matrix differential systems of second order
Transactions of the American Mathematical Society - Tập 122 Số 2 - Trang 289-310
Oscillation and nonoscillation of solutions of second order linear differential equations with integrable coefficients
Transactions of the American Mathematical Society - Tập 144 Số 0 - Trang 197-215
Tổng số: 145
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