Linear transformations on Grassman spaces

Vector Spaces and Linear Transformations

1 Vector spaces A vector space is a nonempty set V , whose objects are called vectors, equipped with two operations, called addition and scalar multiplication: For any two vectors u, v in V and a scalar c, there are unique vectors u + v and cu in V such that the following properties are satisfied. 1. u + v = v + u, 2. (u + v) + w = u + (v + w), 3. There is a vector 0, called the zero vector, su...

Linear Transformations of Euclidean Topological Spaces

For simplicity, we adopt the following rules: X, Y denote sets, n, m, k, i denote natural numbers, r denotes a real number, R denotes an element of RF, K denotes a field, f , f1, f2, g1, g2 denote finite sequences, r1, r2, r3 denote real-valued finite sequences, c1, c2 denote complex-valued finite sequences, and F denotes a function. Let us consider X, Y and let F be a positive yielding partial...

Norm Preserving Extensions of Linear Transformations on Hilbert Spaces

Introduction. Let 77 be a Hubert space and let D be a closed proper subspace of 77. Let 70 be a linear contraction on D to 77. The problem of characterizing the contractions on all of 77 which extend J0 is directly related to the extension problems for unbounded transformations posed and treated by M. G. Krein [2] and R. S. Phillips [3]. In §1 of this paper we establish the following solution o...

Linear Graph Transformations on Spaces of Analytic Functions

Let H be a Hilbert space of analytic functions with multiplier algebra M(H), and let M = {(f, T1f...., Tn−1f) : f ∈ D} be an invariant graph subspace for M(H). Here n ≥ 2, D ⊆ H is a vector-subspace, Ti : D → H are linear transformations that commute with each multiplication operator Mφ ∈ M(H), and M is closed in H. In this paper we investigate the existence of nontrivial common invariant subsp...

On One-Sided Ideals of Rings of Linear Transformations