Sentence examples for be a left regular from inspiring English sources

Let be a left regular sequence of means on and let be a sequence in such that and.

Let ({mu_{n}}) be a left regular sequence of means on X. Suppose that f is an α-contraction on C. Let (epsilon_{n}) be a sequence in ((0, 1)) such that (lim_{n} epsilon_{n}=0).

Let X be a left invariant subspace of L ∞ such that 1 ∈ X, and the function t → 〈 T ( t ) x, y 〉 is an element of X for each x, y ∈ H. Let { μ n } n = 1 ∞ be a left regular sequence of means on X and let { α n } n = 1 ∞ be a sequence in [ 0, 1 ] such that lim n → ∞ α n = 0 and ∑ n = 1 ∞ α n = ∞.

Let X be a left invariant subspace of ℓ ∞ ( S ) such that 1 ∈ X, and the function t ↦ 〈 T ( t ) x, y 〉 is an element of X for each x, y ∈ H. Let { μ n } be a left regular sequence of means on X such that lim n → ∞ ∥ μ n + 1 − μ n ∥ = 0. Let f be an α-contraction on H and A a strongly positive bounded linear operator with coefficient γ ¯.

Let X be a left invariant S -stable subspace of l ∞ ( S ) containing 1, { μ n } be a strongly left regular sequence of means on X such that lim n → ∞ ∥ μ n + 1 − μ n ∥ = 0 and { c n } be the sequence defined by (2.4) with lim sup n → ∞ c n ≤ 0. Suppose the sequences { α n }, { β n }, { γ n } and { δ n } in ( 0, 1 ) satisfy α n + β n + γ n = 1, n ≥ 1.

Let X be a left invariant S -stable subspace of l ∞ ( S ) containing 1, { μ n } be a strongly left regular sequence of means on X such that lim n → ∞ ∥ μ n + 1 − μ n ∥ = 0 and { c n } be the sequence defined by (2.4) with lim sup n → ∞ c n ≤ 0. Suppose the sequences { α n }, { β n } and { γ n } in ( 0, 1 ) satisfy α n + β n + γ n = 1, n ≥ 1.

Let X be a left invariant S -stable subspace of l ∞ ( S ) containing 1, { μ n } be a strongly left regular sequence of means on X such that lim n → ∞ ∥ μ n + 1 − μ n ∥ = 0 and { c n } be the sequence defined in (2.4) with lim sup n → ∞ c n ≤ 0. Suppose the sequences { α n }, { β n }, { γ n } and { δ n } in ( 0, 1 ) satisfy α n + β n + γ n = 1, n ≥ 1.

Let X be a left invariant S Open image in new window-stable subspace of l ∞ (S) containing 1, {μ n } be a strongly left regular sequence of means on X such that limn→∞∥μn+1−μ n ∥=0 and {c n } be the sequence defined by (5).

Let X be a left invariant S Open image in new window-stable subspace of l ∞ (S) containing 1, {μ n } be a strongly left regular sequence of means on X such that lim n →∞∥μn+1−μ n ∥ = 0 and {c n } be the sequence defined by (5).

Let X be a left invariant subspace of l ∞ ( S ) containing 1 such that the mappings s ↦ 〈 T s x, x ∗ 〉 be in X for all x ∈ X and x ∗ ∈ E ∗, and { μ n } be a strongly left regular sequence of means on X.

Let X be a left invariant subspace of l ∞ (S) containing 1 such that the mappings s↦〈T s)x,x∗〉 be in X for all x∈X and x∗∈E∗, and {μ n } be a strongly left regular sequence of means on X[8].