diff --git a/Project.toml b/Project.toml
index 8d1f2d9..030395a 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "InfiniteLinearAlgebra"
 uuid = "cde9dba0-b1de-11e9-2c62-0bab9446c55c"
-version = "0.8.2"
+version = "0.8.3"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
diff --git a/src/InfiniteLinearAlgebra.jl b/src/InfiniteLinearAlgebra.jl
index 80c5912..19203f3 100644
--- a/src/InfiniteLinearAlgebra.jl
+++ b/src/InfiniteLinearAlgebra.jl
@@ -40,7 +40,7 @@ import LazyArrays: AbstractCachedMatrix, AbstractCachedVector, AbstractLazyLayou
                    CachedArray, CachedLayout, CachedMatrix, CachedVector, LazyArrayStyle, LazyLayout,
                    LazyLayouts, LazyMatrix, AbstractPaddedLayout, PaddedColumns, _broadcast_sub_arguments,
                    applybroadcaststyle, applylayout, arguments, cacheddata, paddeddata, resizedata!, simplifiable,
-                   simplify
+                   simplify, islazy, islazy_layout
 
 import LazyBandedMatrices: AbstractLazyBandedBlockBandedLayout, AbstractLazyBandedLayout, ApplyBandedLayout, BlockVec,
                            BroadcastBandedLayout, KronTravBandedBlockBandedLayout, LazyBandedLayout,
diff --git a/src/banded/infbanded.jl b/src/banded/infbanded.jl
index 4956dfd..215104a 100644
--- a/src/banded/infbanded.jl
+++ b/src/banded/infbanded.jl
@@ -323,8 +323,8 @@ ConstRowMatrix(A::AbstractMatrix{T}) where T = ApplyMatrix(*, A[:,1], Ones{T}(1,
 PertConstRowMatrix(A::AbstractMatrix{T}) where T =
     Hcat(_pertdata(A), ApplyMatrix(*, _constrows(A), Ones{T}(1,size(A,2))))
 
-struct ConstRows <: MemoryLayout end
-struct PertConstRows <: MemoryLayout end
+struct ConstRows <: AbstractLazyLayout end
+struct PertConstRows <: AbstractLazyLayout end
 MemoryLayout(::Type{<:ConstRowMatrix}) = ConstRows()
 MemoryLayout(::Type{<:PertConstRowMatrix}) = PertConstRows()
 bandedcolumns(::ConstRows) = BandedToeplitzLayout()
@@ -361,6 +361,11 @@ diagonalconstant(A) = getindex_value(diagonaldata(A))
 supdiagonalconstant(A) = getindex_value(supdiagonaldata(A))
 
 
+islazy_layout(::InfToeplitzLayouts) = Val(true)
+islazy(::BandedMatrix{<:Any,<:Any,OneToInf{Int}}) = Val(true)
+
+
+
 _BandedMatrix(::BandedToeplitzLayout, A::AbstractMatrix) =
     _BandedMatrix(ConstRowMatrix(bandeddata(A)), size(A,1), bandwidths(A)...)
 _BandedMatrix(::PertToeplitzLayout, A::AbstractMatrix) =
diff --git a/src/infql.jl b/src/infql.jl
index 5fa97db..1d74fae 100644
--- a/src/infql.jl
+++ b/src/infql.jl
@@ -401,7 +401,7 @@ function initialadaptiveQLblock(A::AbstractMatrix{T}, tol) where T
         Ll = ql(A[checkinds:2N,checkinds:2N]).L[2:j-checkinds+1,2:j-checkinds+1]
         # compare bottom right sections and stop if desired level of convergence achieved
         Lerr = norm(Ll-Ls,2)
-        if N == maxN
+        if N >= maxN
             error("Reached max. iterations in adaptive QL without convergence to desired tolerance.")
         end
         Ls = Ll
@@ -449,7 +449,7 @@ function cache_filldata!(A::AdaptiveQLFactors{T}, inds::UnitRange{Int}) where T
         Ll = ql(A.M[checkinds:2N,checkinds:2N]).L[2:j-checkinds+1,2:j-checkinds+1]
         # compare bottom right sections and stop if desired level of convergence achieved
         Lerr = norm(Ll-Ls,2)
-        if N == maxN
+        if N >= maxN
             error("Reached max. iterations in adaptive QL without convergence to desired tolerance.")
         end
         Ls = Ll
@@ -470,7 +470,7 @@ function cache_filldata!(A::AdaptiveQLTau{T}, inds::UnitRange{Int}) where T
         Ll = ql(A.M[checkinds:2N,checkinds:2N]).L[2:j-checkinds+1,2:j-checkinds+1]
         # compare bottom right sections and stop if desired level of convergence achieved
         Lerr = norm(Ll-Ls,2)
-        if N == maxN
+        if N >= maxN
             error("Reached max. iterations in adaptive QL without convergence to desired tolerance.")
         end
         Ls = Ll
diff --git a/test/test_infbanded.jl b/test/test_infbanded.jl
index f2db878..804e17e 100644
--- a/test/test_infbanded.jl
+++ b/test/test_infbanded.jl
@@ -34,8 +34,10 @@ using Base: oneto
     @testset "∞-Toeplitz" begin
         A = BandedMatrix(1 => Fill(2im,∞), 2 => Fill(-1,∞), 3 => Fill(2,∞), -2 => Fill(-4,∞), -3 => Fill(-2im,∞))
         @test A isa InfToeplitz
-        @test MemoryLayout(typeof(A.data)) == ConstRows()
-        @test MemoryLayout(typeof(A)) == BandedToeplitzLayout()
+        @test MemoryLayout(A.data) == ConstRows()
+        @test MemoryLayout(A) == BandedToeplitzLayout()
+        @test LazyArrays.islazy(A) == Val(true)
+
         V = view(A,:,3:∞)
         @test MemoryLayout(typeof(bandeddata(V))) == ConstRows()
         @test MemoryLayout(typeof(V)) == BandedToeplitzLayout()
@@ -166,6 +168,7 @@ using Base: oneto
 
     @testset "Banded * PaddedMatrix" begin
         A = Eye(∞)[2:∞,:]
+        @test LazyArrays.islazy(A) == Val(true)
         B = PaddedArray(randn(3,3),ℵ₀,ℵ₀)
         @test (A*B)[1:10,1:10] ≈ A[1:10,1:10] * B[1:10,1:10]
     end
diff --git a/test/test_infql.jl b/test/test_infql.jl
index ca42293..cc1f4f3 100644
--- a/test/test_infql.jl
+++ b/test/test_infql.jl
@@ -219,6 +219,10 @@ using ArrayLayouts: TriangularLayout, UnknownLayout
             @test (L*b)[1:6] == ApplyArray(*,L,b)[1:6] == [0. , -5.25,  -7.833333333333333, -2.4166666666666666, -1., 0.]
             @test size(ql(A).τ) == (ℵ₀, )
         end
+        @testset "Naive extremely long / infinite loop protection" begin
+            A = _BandedMatrix(Vcat((((0:∞)))', (((1:∞)).+1/4)', Ones(1,∞)./3), ℵ₀, 1, 1)
+            @test_throws ErrorException("Reached max. iterations in adaptive QL without convergence to desired tolerance.") ql(A)
+        end
         @testset "Explicit tolerance tests" begin
             Asym = LinearAlgebra.SymTridiagonal([[1.,2.]; Fill(3.,∞)], [[1., 2.]; Fill(1.,∞)])
             Aplain = LinearAlgebra.Tridiagonal([[1., 2.]; Fill(1.,∞)], [[1.,2.]; Fill(3.,∞)], [[1., 2.]; Fill(1.,∞)])
@@ -287,4 +291,4 @@ using ArrayLayouts: TriangularLayout, UnknownLayout
         Q,L = ql(A)
         @test (Q*L)[1:10,1:10] ≈ A[1:10,1:10]
     end
-end
+end
\ No newline at end of file